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Author ID: polacik.peter Recent zbMATH articles by "Poláčik, Peter"
Published as: Poláčik, Peter; Poláčik, P.; Polácik, Peter; Polacik, Peter; Poláçik, Peter; Polácik, P.
External Links: MGP
Documents Indexed: 110 Publications since 1987, including 2 Books
2 Contributions as Editor
Reviewing Activity: 155 Reviews
Co-Authors: 40 Co-Authors with 76 Joint Publications
1,266 Co-Co-Authors
all top 5

Serials

14 Journal of Differential Equations
10 Journal of Dynamics and Differential Equations
8 Discrete and Continuous Dynamical Systems
6 Communications in Partial Differential Equations
5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
5 SIAM Journal on Mathematical Analysis
3 Archive for Rational Mechanics and Analysis
3 Indiana University Mathematics Journal
3 Journal of Functional Analysis
3 Journal für die Reine und Angewandte Mathematik
3 Mathematische Annalen
3 Proceedings of the American Mathematical Society
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
2 Memoirs of the American Mathematical Society
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2 Differential and Integral Equations
2 Acta Mathematica Universitatis Comenianae. New Series
2 Advances in Differential Equations
2 Nonlinear Analysis. Theory, Methods & Applications
1 Journal d’Analyse Mathématique
1 Journal of Mathematical Biology
1 Nonlinearity
1 Commentationes Mathematicae Universitatis Carolinae
1 Duke Mathematical Journal
1 Mathematische Zeitschrift
1 Transactions of the American Mathematical Society
1 Asymptotic Analysis
1 Mathematica Bohemica
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Tatra Mountains Mathematical Publications
1 Electronic Journal of Qualitative Theory of Differential Equations
1 Journal of the European Mathematical Society (JEMS)
1 Journal of Evolution Equations
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
1 Journal of Fixed Point Theory and Applications
1 Networks and Heterogeneous Media
1 Discrete and Continuous Dynamical Systems. Series S
1 SN Partial Differential Equations and Applications

Publications by Year

Citations contained in zbMATH Open

102 Publications have been cited 1,817 times in 1,038 Documents Cited by Year
Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
230
2007
The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035
Hutson, V.; Mischaikow, K.; Poláčik, P.
104
2001
Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
84
2007
On bounded and unbounded global solutions of a supercritical semilinear heat equation. Zbl 1055.35055
Poláčik, Peter; Yanagida, Eiji
68
2003
Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Zbl 0755.58039
Poláčik, P.; Tereščák, I.
57
1991
Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0786.58002
Poláčik, P.; Tereščák, Ignác
52
1993
Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. Zbl 0684.34064
Poláčik, Peter
45
1989
Competing species near a degenerate limit. Zbl 1043.35080
Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P.
40
2003
Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball. Zbl 0839.35059
Chen, Xu-Yan; Poláčik, Peter
39
1996
Parabolic equations: Asymptotic behavior and dynamics on invariant manifolds. Zbl 1002.35001
Poláčik, P.
37
2002
Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060
Fiedler, Bernold; Poláčik, Peter
34
1990
Nonconvergent bounded trajectories in semilinear heat equations. Zbl 0845.35054
Poláčik, Peter; Rybakowski, Krzysztof P.
33
1996
On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Zbl 1178.35098
Földes, J.; Poláčik, Peter
33
2009
The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension. Zbl 0868.35062
Brunovský, P.; Poláčik, P.
32
1997
Threshold solutions and sharp transitions for nonautonomous parabolic equations on \({\mathbb{R}^N}\). Zbl 1262.35130
Poláčik, P.
30
2011
Loops and branches of coexistence states in a Lotka–Volterra competition model. Zbl 1154.35011
Lou, Yuan; Martínez, Salomé; Poláčik, Peter
30
2006
Convergence in general periodic parabolic equations in one space dimension. Zbl 0796.35009
Brunovský, P.; Poláčik, P.; Sandstede, B.
30
1992
A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation. Zbl 1092.35045
Poláčik, Peter; Quittner, Pavol
29
2006
Convergence to equilibrium for semilinear parabolic problems in \(\mathbb{R}^N\). Zbl 1021.35013
Busca, J.; Jendoubi, M. A.; Poláčik, P.
28
2002
Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. Zbl 1215.35041
Bartsch, Thomas; Poláčik, Peter; Quittner, Pavol
28
2011
Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains. Zbl 1024.35046
Poláčik, P.; Simondon, F.
25
2002
Locally uniform convergence to an equilibrium for nonlinear parabolic equations on \(\mathbb{R}^N\). Zbl 1336.35207
Du, Yihong; Poláčik, Peter
25
2015
Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. Part I: A general quasiconvergence theorem and its consequences. Zbl 1345.35052
Matano, H.; Poláčik, P.
24
2016
Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on \(\mathbb{R}\). Zbl 1450.35002
Poláčik, Peter
24
2020
A Liouville property and quasiconvergence for a semilinear heat equation. Zbl 1068.35044
Poláčik, P.; Yanagida, E.
23
2005
Symmetry and convergence properties for nonnegative solutions of nonautonomous reaction-diffusion problems. Zbl 0811.35049
Hess, Peter; Poláčik, P.
23
1994
Convergence to a positive equilibrium for some nonlinear evolution equations in a ball. Zbl 0824.35011
Haraux, A.; Poláčik, P.
21
1992
Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on \(\mathbb{R}\). Zbl 0987.35079
Feireisl, Eduard; Poláčik, Peter
21
2000
Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations. Zbl 1139.35046
Húska, Juraj; Poláčik, Peter; Safonov, Mikhail V.
21
2007
Erratum to: Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0791.58008
Poláčik, P.; Tereščák, I.
20
1994
Monotonicity of stable solutions in shadow systems. Zbl 0981.35018
Ni, Wei-Ming; Polácik, Peter; Yanagida, Eiji
19
2001
Complicated dynamics in scalar semilinear parabolic equations in higher space dimension. Zbl 0738.35027
Poláčik, Peter
18
1991
Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. Zbl 0797.58077
Hess, Peter; Poláčik, Peter
18
1993
Immediate regularization after blow-up. Zbl 1102.35053
Fila, Marek; Matano, Hiroshi; Polácik, Peter
17
2005
Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). I: Asymptotic symmetry for the Cauchy problem. Zbl 1083.35045
Poláčik, P.
16
2005
High-dimensional \(\omega\)-limit sets and chaos in scalar parabolic equations. Zbl 0830.35060
Poláčik, Peter
14
1995
Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains. Zbl 1171.35063
Poláčik, Peter
14
2007
Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on \({\mathbb{R}}\). Zbl 1319.35097
Poláčik, P.
14
2015
Planar propagating terraces and the asymptotic one-dimensional symmetry of solutions of semilinear parabolic equations. Zbl 1516.35089
Poláčik, P.
14
2017
Convergence to a steady state for asymptotically autonomous semilinear heat equations on \(\mathbb R^N\). Zbl 1263.35035
Földes, Juraj; Poláčik, P.
13
2011
Symmetry properties of positive solutions of parabolic equations: a survey. Zbl 1213.35042
Poláčik, P.
13
2009
Liouville type theorems and complete blow-up for indefinite superlinear parabolic equations. Zbl 1093.35037
Poláčik, Peter; Quittner, Pavol
13
2005
Gradient-like structure and Morse decompositions for time-periodic one- dimensional parabolic equations. Zbl 0822.35073
Chen, Xu-Yan; Poláčik, Peter
12
1995
On the local structure of \(\omega\)-limit sets of maps. Zbl 0889.34048
Brunovský, P.; Poláčik, P.
12
1997
The principal Floquet bundle and exponential separation for linear parabolic equations. Zbl 1128.35353
Húska, Juraj; Poláčik, Peter
12
2004
Threshold behavior and non-quasiconvergent solutions with localized initial data for bistable reaction-diffusion equations. Zbl 1456.35039
Poláčik, P.
12
2016
Existence of quasiperiodic solutions of elliptic equations on \(\mathbb{R}^{N + 1}\) via center manifold and KAM theorems. Zbl 1372.35016
Poláčik, Peter; Valdebenito, Darío A.
12
2017
Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). II: Entire solutions. Zbl 1128.35051
Poláčik, P.
11
2006
Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Zbl 0926.35060
Dancer, E. N.; Poláčik, P.
11
1999
Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping. Zbl 1046.37045
Jendoubi, M. A.; Poláčik, P.
10
2003
Zeros of complex caloric functions and singularities of complex viscous Burgers equation. Zbl 1188.35153
Poláčik, P.; Šverák, V.
10
2008
Morse indices and bifurcations of positive solutions of \(\Delta u+f(u)=0\) on \(\mathbb R^ N\). Zbl 1101.35321
Poláčik, Peter
10
2001
Realization of any finite jet in a scalar semilinear parabolic equation on the ball in \(\mathbb{R}^ 3\). Zbl 0774.35041
Poláčik, Peter
9
1991
Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics. Zbl 1316.35148
Poláčik, Peter; Yanagida, Eiji
9
2014
Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation. Zbl 1174.35403
Poláčik, P.; Yanagida, E.
8
2004
Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030
Fila, Marek; Poláčik, Peter
8
1999
On uniqueness of positive entire solutions and other properties of linear parabolic equations. Zbl 1067.35030
Poláčik, P.
8
2005
Imbedding of any vector field in a scalar semilinear parabolic equation. Zbl 0755.35046
Poláčik, P.
8
1992
An entire solution of a bistable parabolic equation on \(\mathbb{R}\) with two colliding pulses. Zbl 1362.35152
Matano, H.; Poláčik, P.
8
2017
Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations. Zbl 1334.35130
Poláčik, Peter
8
2015
Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. II: Generic nonlinearities. Zbl 1439.35200
Matano, H.; Poláčik, P.
8
2020
Domains of attraction of equilibria and monotonicity of convergent trajectories in parabolic systems admitting strong comparison principle. Zbl 0667.35036
Poláčik, Peter
7
1989
The parabolic logistic equation with blow-up initial and boundary values. Zbl 1308.35127
Du, Yihong; Peng, Rui; Poláçik, Peter
7
2012
Generic hyperbolicity in one-dimensional reaction-diffusion equations with general boundary conditions. Zbl 0639.35039
Poláčik, Peter
6
1987
Group actions on strongly monotone dynamical systems. Zbl 0642.58031
Mierczyński, Janusz; Poláčik, Peter
6
1989
Global solutions of a semilinear parabolic equation. Zbl 0953.35065
Fila, Marek; Poláčik, Peter
6
1999
Transversal and nontransversal intersections of stable and unstable manifolds in reaction diffusion equations on symmetric domains. Zbl 0809.35041
Poláčik, Peter
6
1994
Entire solutions and a Liouville theorem for a class of parabolic equations on the real line. Zbl 1448.35304
Poláčik, P.
6
2020
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. Zbl 1393.35076
Pauthier, Antoine; Poláčik, Peter
6
2018
Exponential separation and principal Floquet bundles for linear parabolic equations on \(\mathbb R^N\). Zbl 1170.35021
Húska, Juraj; Poláčik, Peter
5
2008
Imbedding vector fields in scalar parabolic Dirichlet BVPs. Zbl 0852.35074
Poláčik, Peter; Rybakowski, Krzysztof
5
1995
Symmetry of nonnegative solutions of elliptic equations via a result of Serrin. Zbl 1241.35083
Poláčik, P.
5
2011
On symmetry of nonnegative solutions of elliptic equations. Zbl 1241.35073
Poláčik, P.
5
2012
Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation. Zbl 0865.35065
Poláčik, Peter; Šošovička, Vladimír
5
1996
Existence of \(L^1\)-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054
Fila, Marek; Matano, Hiroshi; Poláčik, Peter
5
2002
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations. Zbl 1010.35009
Poláčik, P.
5
2002
Nonnegative solutions with a nontrivial nodal set for elliptic equations on smooth symmetric domains. Zbl 1286.35109
Poláčik, P.; Terracini, Susanna
5
2014
Entire and ancient solutions of a supercritical semilinear heat equation. Zbl 1458.35228
Poláčik, Peter; Quittner, Pavol
5
2021
Generic hyperbolicity for reaction diffusion equations on symmetric domains. Zbl 0622.35005
Brunovský, Pavol; Poláčik, Peter
4
1987
Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip. Zbl 0744.35013
Brunovský, P.; Mora, X.; Poláčik, P.; Solà-Morales, J.
4
1991
Global unbounded solutions of the Fujita equation in the intermediate range. Zbl 1319.35109
Poláčik, Peter; Yanagida, Eiji
4
2014
On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains. Zbl 1285.35034
Poláčik, Peter
4
2014
Existence of quasiperiodic solutions of elliptic equations on the entire space with a quadratic nonlinearity. Zbl 1439.35026
Poláčik, Peter; Valdebenito, Darío A.
4
2020
Convergence of anisotropically decaying solutions of a supercritical semilinear heat equation. Zbl 1197.35150
Poláčik, Peter; Yanagida, Eiji
3
2009
Existence of stable subharmonic solutions for reaction-diffusion equations. Zbl 0981.35023
Poláčik, Peter; Yanagida, Eiji
3
2001
Immediate regularization after blow-up. Zbl 1108.35092
Fila, M.; Matano, H.; Poláčik, P.
3
2005
Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations. Zbl 0714.58043
Poláčik, P.
3
1990
Propagating terraces in a proof of the Gibbons conjecture and related results. Zbl 1366.35093
Poláčik, P.
3
2017
Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation. Zbl 1153.35014
Poláčik, Peter; Quittner, Pavol
3
2008
Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Zbl 1152.35391
Húska, J.; Poláčik, P.; Safonov, M. V.
3
2005
Existence of partially localized quasiperiodic solutions of homogeneous elliptic equations on \(\mathbb{R}^{N+1}\). Zbl 1479.35412
Poláčik, Peter; Valdebenito, Darío A.
3
2020
Persistent saddle connections in a class of reaction-diffusion equations. Zbl 0936.35097
Poláčik, Peter
2
1999
Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. Zbl 0993.35051
Poláčik, Peter; Yanagida, Eiji
2
2002
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows. Zbl 0724.58054
Poláčik, Peter
2
1990
Realization of the dynamic of ODE’s in scalar parabolic PDEs. Zbl 0811.35065
Poláčik, Peter
2
1994
Positivity and symmetry of nonnegative solutions of semilinear elliptic equations on planar domains. Zbl 1243.35074
Poláčik, P.
2
2012
On the multiplicity of self-similar solutions of the semilinear heat equation. Zbl 1428.35170
Poláčik, P.; Quittner, P.
2
2020
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. II: Equal limits at infinity. Zbl 1473.35056
Pauthier, Antoine; Poláčik, Peter
2
2021
On asymptotically symmetric parabolic equations. Zbl 1262.35041
Földes, Juraj; Poláčik, Peter
2
2012
Equilibria with a nontrivial nodal set and the dynamics of parabolic equations on symmetric domains. Zbl 1328.35109
Földes, J.; Poláčik, P.
1
2015
The existence of partially localized periodic-quasiperiodic solutions and related KAM-type results for elliptic equations on the entire space. (https://www.zentralblatt-math.org/math/correction/.) Zbl 1501.35148
Poláčik, Peter; Valdebenito, Darío A.
1
2022
Entire and ancient solutions of a supercritical semilinear heat equation. Zbl 1458.35228
Poláčik, Peter; Quittner, Pavol
5
2021
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. II: Equal limits at infinity. Zbl 1473.35056
Pauthier, Antoine; Poláčik, Peter
2
2021
Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on \(\mathbb{R}\). Zbl 1450.35002
Poláčik, Peter
24
2020
Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. II: Generic nonlinearities. Zbl 1439.35200
Matano, H.; Poláčik, P.
8
2020
Entire solutions and a Liouville theorem for a class of parabolic equations on the real line. Zbl 1448.35304
Poláčik, P.
6
2020
Existence of quasiperiodic solutions of elliptic equations on the entire space with a quadratic nonlinearity. Zbl 1439.35026
Poláčik, Peter; Valdebenito, Darío A.
4
2020
Existence of partially localized quasiperiodic solutions of homogeneous elliptic equations on \(\mathbb{R}^{N+1}\). Zbl 1479.35412
Poláčik, Peter; Valdebenito, Darío A.
3
2020
On the multiplicity of self-similar solutions of the semilinear heat equation. Zbl 1428.35170
Poláčik, P.; Quittner, P.
2
2020
Some generic properties of Schrödinger operators with radial potentials. Zbl 1436.35099
Poláčik, Peter; Valdebenito, Darío A.
1
2019
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. Zbl 1393.35076
Pauthier, Antoine; Poláčik, Peter
6
2018
Planar propagating terraces and the asymptotic one-dimensional symmetry of solutions of semilinear parabolic equations. Zbl 1516.35089
Poláčik, P.
14
2017
Existence of quasiperiodic solutions of elliptic equations on \(\mathbb{R}^{N + 1}\) via center manifold and KAM theorems. Zbl 1372.35016
Poláčik, Peter; Valdebenito, Darío A.
12
2017
An entire solution of a bistable parabolic equation on \(\mathbb{R}\) with two colliding pulses. Zbl 1362.35152
Matano, H.; Poláčik, P.
8
2017
Propagating terraces in a proof of the Gibbons conjecture and related results. Zbl 1366.35093
Poláčik, P.
3
2017
Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. Part I: A general quasiconvergence theorem and its consequences. Zbl 1345.35052
Matano, H.; Poláčik, P.
24
2016
Threshold behavior and non-quasiconvergent solutions with localized initial data for bistable reaction-diffusion equations. Zbl 1456.35039
Poláčik, P.
12
2016
Locally uniform convergence to an equilibrium for nonlinear parabolic equations on \(\mathbb{R}^N\). Zbl 1336.35207
Du, Yihong; Poláčik, Peter
25
2015
Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on \({\mathbb{R}}\). Zbl 1319.35097
Poláčik, P.
14
2015
Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations. Zbl 1334.35130
Poláčik, Peter
8
2015
Equilibria with a nontrivial nodal set and the dynamics of parabolic equations on symmetric domains. Zbl 1328.35109
Földes, J.; Poláčik, P.
1
2015
Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics. Zbl 1316.35148
Poláčik, Peter; Yanagida, Eiji
9
2014
Nonnegative solutions with a nontrivial nodal set for elliptic equations on smooth symmetric domains. Zbl 1286.35109
Poláčik, P.; Terracini, Susanna
5
2014
Global unbounded solutions of the Fujita equation in the intermediate range. Zbl 1319.35109
Poláčik, Peter; Yanagida, Eiji
4
2014
On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains. Zbl 1285.35034
Poláčik, Peter
4
2014
The parabolic logistic equation with blow-up initial and boundary values. Zbl 1308.35127
Du, Yihong; Peng, Rui; Poláçik, Peter
7
2012
On symmetry of nonnegative solutions of elliptic equations. Zbl 1241.35073
Poláčik, P.
5
2012
Positivity and symmetry of nonnegative solutions of semilinear elliptic equations on planar domains. Zbl 1243.35074
Poláčik, P.
2
2012
On asymptotically symmetric parabolic equations. Zbl 1262.35041
Földes, Juraj; Poláčik, Peter
2
2012
Threshold solutions and sharp transitions for nonautonomous parabolic equations on \({\mathbb{R}^N}\). Zbl 1262.35130
Poláčik, P.
30
2011
Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. Zbl 1215.35041
Bartsch, Thomas; Poláčik, Peter; Quittner, Pavol
28
2011
Convergence to a steady state for asymptotically autonomous semilinear heat equations on \(\mathbb R^N\). Zbl 1263.35035
Földes, Juraj; Poláčik, P.
13
2011
Symmetry of nonnegative solutions of elliptic equations via a result of Serrin. Zbl 1241.35083
Poláčik, P.
5
2011
On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Zbl 1178.35098
Földes, J.; Poláčik, Peter
33
2009
Symmetry properties of positive solutions of parabolic equations: a survey. Zbl 1213.35042
Poláčik, P.
13
2009
Convergence of anisotropically decaying solutions of a supercritical semilinear heat equation. Zbl 1197.35150
Poláčik, Peter; Yanagida, Eiji
3
2009
Zeros of complex caloric functions and singularities of complex viscous Burgers equation. Zbl 1188.35153
Poláčik, P.; Šverák, V.
10
2008
Exponential separation and principal Floquet bundles for linear parabolic equations on \(\mathbb R^N\). Zbl 1170.35021
Húska, Juraj; Poláčik, Peter
5
2008
Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation. Zbl 1153.35014
Poláčik, Peter; Quittner, Pavol
3
2008
Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
230
2007
Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051
Poláčik, Peter; Quittner, Pavol; Souplet, Philippe
84
2007
Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations. Zbl 1139.35046
Húska, Juraj; Poláčik, Peter; Safonov, Mikhail V.
21
2007
Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains. Zbl 1171.35063
Poláčik, Peter
14
2007
Loops and branches of coexistence states in a Lotka–Volterra competition model. Zbl 1154.35011
Lou, Yuan; Martínez, Salomé; Poláčik, Peter
30
2006
A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation. Zbl 1092.35045
Poláčik, Peter; Quittner, Pavol
29
2006
Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). II: Entire solutions. Zbl 1128.35051
Poláčik, P.
11
2006
A Liouville property and quasiconvergence for a semilinear heat equation. Zbl 1068.35044
Poláčik, P.; Yanagida, E.
23
2005
Immediate regularization after blow-up. Zbl 1102.35053
Fila, Marek; Matano, Hiroshi; Polácik, Peter
17
2005
Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). I: Asymptotic symmetry for the Cauchy problem. Zbl 1083.35045
Poláčik, P.
16
2005
Liouville type theorems and complete blow-up for indefinite superlinear parabolic equations. Zbl 1093.35037
Poláčik, Peter; Quittner, Pavol
13
2005
On uniqueness of positive entire solutions and other properties of linear parabolic equations. Zbl 1067.35030
Poláčik, P.
8
2005
Immediate regularization after blow-up. Zbl 1108.35092
Fila, M.; Matano, H.; Poláčik, P.
3
2005
Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Zbl 1152.35391
Húska, J.; Poláčik, P.; Safonov, M. V.
3
2005
The principal Floquet bundle and exponential separation for linear parabolic equations. Zbl 1128.35353
Húska, Juraj; Poláčik, Peter
12
2004
Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation. Zbl 1174.35403
Poláčik, P.; Yanagida, E.
8
2004
On bounded and unbounded global solutions of a supercritical semilinear heat equation. Zbl 1055.35055
Poláčik, Peter; Yanagida, Eiji
68
2003
Competing species near a degenerate limit. Zbl 1043.35080
Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P.
40
2003
Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping. Zbl 1046.37045
Jendoubi, M. A.; Poláčik, P.
10
2003
Parabolic equations: Asymptotic behavior and dynamics on invariant manifolds. Zbl 1002.35001
Poláčik, P.
37
2002
Convergence to equilibrium for semilinear parabolic problems in \(\mathbb{R}^N\). Zbl 1021.35013
Busca, J.; Jendoubi, M. A.; Poláčik, P.
28
2002
Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains. Zbl 1024.35046
Poláčik, P.; Simondon, F.
25
2002
Existence of \(L^1\)-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054
Fila, Marek; Matano, Hiroshi; Poláčik, Peter
5
2002
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations. Zbl 1010.35009
Poláčik, P.
5
2002
Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. Zbl 0993.35051
Poláčik, Peter; Yanagida, Eiji
2
2002
The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035
Hutson, V.; Mischaikow, K.; Poláčik, P.
104
2001
Monotonicity of stable solutions in shadow systems. Zbl 0981.35018
Ni, Wei-Ming; Polácik, Peter; Yanagida, Eiji
19
2001
Morse indices and bifurcations of positive solutions of \(\Delta u+f(u)=0\) on \(\mathbb R^ N\). Zbl 1101.35321
Poláčik, Peter
10
2001
Existence of stable subharmonic solutions for reaction-diffusion equations. Zbl 0981.35023
Poláčik, Peter; Yanagida, Eiji
3
2001
Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on \(\mathbb{R}\). Zbl 0987.35079
Feireisl, Eduard; Poláčik, Peter
21
2000
Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Zbl 0926.35060
Dancer, E. N.; Poláčik, P.
11
1999
Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030
Fila, Marek; Poláčik, Peter
8
1999
Global solutions of a semilinear parabolic equation. Zbl 0953.35065
Fila, Marek; Poláčik, Peter
6
1999
Persistent saddle connections in a class of reaction-diffusion equations. Zbl 0936.35097
Poláčik, Peter
2
1999
The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension. Zbl 0868.35062
Brunovský, P.; Poláčik, P.
32
1997
On the local structure of \(\omega\)-limit sets of maps. Zbl 0889.34048
Brunovský, P.; Poláčik, P.
12
1997
Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball. Zbl 0839.35059
Chen, Xu-Yan; Poláčik, Peter
39
1996
Nonconvergent bounded trajectories in semilinear heat equations. Zbl 0845.35054
Poláčik, Peter; Rybakowski, Krzysztof P.
33
1996
Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation. Zbl 0865.35065
Poláčik, Peter; Šošovička, Vladimír
5
1996
High-dimensional \(\omega\)-limit sets and chaos in scalar parabolic equations. Zbl 0830.35060
Poláčik, Peter
14
1995
Gradient-like structure and Morse decompositions for time-periodic one- dimensional parabolic equations. Zbl 0822.35073
Chen, Xu-Yan; Poláčik, Peter
12
1995
Imbedding vector fields in scalar parabolic Dirichlet BVPs. Zbl 0852.35074
Poláčik, Peter; Rybakowski, Krzysztof
5
1995
Symmetry and convergence properties for nonnegative solutions of nonautonomous reaction-diffusion problems. Zbl 0811.35049
Hess, Peter; Poláčik, P.
23
1994
Erratum to: Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0791.58008
Poláčik, P.; Tereščák, I.
20
1994
Transversal and nontransversal intersections of stable and unstable manifolds in reaction diffusion equations on symmetric domains. Zbl 0809.35041
Poláčik, Peter
6
1994
Realization of the dynamic of ODE’s in scalar parabolic PDEs. Zbl 0811.35065
Poláčik, Peter
2
1994
Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0786.58002
Poláčik, P.; Tereščák, Ignác
52
1993
Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. Zbl 0797.58077
Hess, Peter; Poláčik, Peter
18
1993
Convergence in general periodic parabolic equations in one space dimension. Zbl 0796.35009
Brunovský, P.; Poláčik, P.; Sandstede, B.
30
1992
Convergence to a positive equilibrium for some nonlinear evolution equations in a ball. Zbl 0824.35011
Haraux, A.; Poláčik, P.
21
1992
Imbedding of any vector field in a scalar semilinear parabolic equation. Zbl 0755.35046
Poláčik, P.
8
1992
Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Zbl 0755.58039
Poláčik, P.; Tereščák, I.
57
1991
Complicated dynamics in scalar semilinear parabolic equations in higher space dimension. Zbl 0738.35027
Poláčik, Peter
18
1991
Realization of any finite jet in a scalar semilinear parabolic equation on the ball in \(\mathbb{R}^ 3\). Zbl 0774.35041
Poláčik, Peter
9
1991
Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip. Zbl 0744.35013
Brunovský, P.; Mora, X.; Poláčik, P.; Solà-Morales, J.
4
1991
Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060
Fiedler, Bernold; Poláčik, Peter
34
1990
Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations. Zbl 0714.58043
Poláčik, P.
3
1990
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows. Zbl 0724.58054
Poláčik, Peter
2
1990
Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. Zbl 0684.34064
Poláčik, Peter
45
1989
Domains of attraction of equilibria and monotonicity of convergent trajectories in parabolic systems admitting strong comparison principle. Zbl 0667.35036
Poláčik, Peter
7
1989
Group actions on strongly monotone dynamical systems. Zbl 0642.58031
Mierczyński, Janusz; Poláčik, Peter
6
1989
...and 2 more Documents
all top 5

Cited by 1,020 Authors

56 Poláčik, Peter
33 Lou, Yuan
22 Shen, Wenxian
20 Wang, Yi
18 Yanagida, Eiji
16 Winkler, Michael
15 Souplet, Philippe
13 Fila, Marek
13 Mizoguchi, Noriko
13 Peng, Rui
13 Quittner, Pavol
13 Wei, Juncheng
12 Matano, Hiroshi
12 Obaya, Rafael
12 Weth, Tobias
11 Du, Yihong
11 Lam, King-Yeung
11 Lou, Bendong
11 Mierczyński, Janusz
11 Phan, Quoc Hung
11 Wang, Zhi Cheng
10 Ishige, Kazuhiro
10 Jendoubi, Mohamed Ali
10 Jiang, Jifa
10 Li, Wan-Tong
10 Zhao, Xiao-Qiang
9 Duong, Anh Tuan
9 Hamel, François
9 Sanz, Ana M.
9 Villavert, John
9 Zhou, Maolin
9 Zou, Wenming
8 Cantrell, Robert Stephen
8 Cosner, Chris
8 Dai, Wei
8 Giletti, Thomas
8 Guo, Zongming
8 Yi, Taishan
7 Chill, Ralph
7 Földes, Juraj
7 Harrabi, Abdellaziz
7 Liu, Shuang
7 Peng, Shaolong
7 Ruan, Shigui
7 Shi, Junping
7 Smith, Hal Leslie
7 Valdebenito, Darío A.
7 Vishnevskii, Mikhail P.
7 Wang, Yuxia
7 Zhang, Zhitao
6 Bo, Wei-Jian
6 Dancer, Edward Norman
6 Ding, Weiwei
6 Kawakami, Tatsuki
6 Langa, Jose’ Antonio
6 Lin, Guo
6 Nadin, Grégoire
6 Qin, Guolin
6 Wu, Hao
6 Wu, Jianhua
6 Yang, Hui
6 Zhang, Zhengce
6 Zhou, Dun
5 Alfaro, Matthieu
5 Berestycki, Henri
5 Chen, Wenxiong
5 Ducrot, Arnaud
5 Fiedler, Bernold
5 García-Melián, Jorge
5 Giga, Yoshikazu
5 Grasselli, Maurizio
5 Huang, Haochuan
5 Huang, Rui
5 Jänig, Axel
5 Joly, Romain
5 Li, Congming
5 Li, Kui
5 Mtiri, Foued
5 Nolasco de Carvalho, Alexandre
5 Raugel, Geneviève
5 Rodríguez-Bernal, Aníbal
5 Roquejoffre, Jean-Michel
5 Saldaña, Alberto
5 Vazquez, Juan Luis
5 Wang, Mingxin
5 Wu, Leyun
5 Yao, Jinxiang
5 Zhang, Liang
4 Bao, Jiguang
4 Bidaut-Veron, Marie-Françoise
4 Brunovský, Pavol
4 Castorina, Daniele
4 Cholewa, Jan W.
4 Del Pino, Manuel A.
4 Dlotko, Tomasz W.
4 Du, Lijun
4 Dupaigne, Louis
4 Farina, Alberto
4 Fujishima, Yohei
4 Húska, Juraj
...and 920 more Authors
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Cited in 178 Serials

152 Journal of Differential Equations
58 Journal of Dynamics and Differential Equations
53 Journal of Mathematical Analysis and Applications
47 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
33 Calculus of Variations and Partial Differential Equations
33 Discrete and Continuous Dynamical Systems
25 Communications on Pure and Applied Analysis
21 Journal of Functional Analysis
20 Journal of Mathematical Biology
19 Nonlinear Analysis. Real World Applications
19 Discrete and Continuous Dynamical Systems. Series B
18 Transactions of the American Mathematical Society
17 Journal de Mathématiques Pures et Appliquées. Neuvième Série
16 Proceedings of the American Mathematical Society
16 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
15 Mathematische Annalen
14 Nonlinearity
14 SIAM Journal on Mathematical Analysis
13 ZAMP. Zeitschrift für angewandte Mathematik und Physik
13 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
13 Communications in Contemporary Mathematics
12 Advances in Mathematics
12 Communications in Partial Differential Equations
12 NoDEA. Nonlinear Differential Equations and Applications
11 Annali di Matematica Pura ed Applicata. Serie Quarta
11 Journal of Evolution Equations
10 Archive for Rational Mechanics and Analysis
9 Science China. Mathematics
8 Bulletin of Mathematical Biology
8 Advances in Nonlinear Analysis
7 Journal d’Analyse Mathématique
7 Applied Mathematics Letters
7 Advances in Difference Equations
6 Applicable Analysis
6 Siberian Mathematical Journal
6 Complex Variables and Elliptic Equations
6 Journal of Biological Dynamics
6 Discrete and Continuous Dynamical Systems. Series S
5 Mathematische Nachrichten
5 Memoirs of the American Mathematical Society
5 Journal of Difference Equations and Applications
5 Journal of Fixed Point Theory and Applications
4 Mathematical Biosciences
4 Mathematical Methods in the Applied Sciences
4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
4 Mathematische Zeitschrift
4 Acta Applicandae Mathematicae
4 SIAM Journal on Applied Mathematics
4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
4 Electronic Journal of Differential Equations (EJDE)
4 Revista Matemática Complutense
4 Advanced Nonlinear Studies
4 Milan Journal of Mathematics
4 Mathematical Biosciences and Engineering
4 Boundary Value Problems
4 SN Partial Differential Equations and Applications
3 Communications in Mathematical Physics
3 Rocky Mountain Journal of Mathematics
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3 Archiv der Mathematik
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3 Physica D
3 Journal of Nonlinear Science
3 Topological Methods in Nonlinear Analysis
3 Journal of the European Mathematical Society (JEMS)
3 Acta Mathematica Sinica. English Series
3 Acta Mathematica Scientia. Series B. (English Edition)
3 Journal of Elliptic and Parabolic Equations
3 AIMS Mathematics
3 Mathematics in Engineering
2 Bulletin of the Australian Mathematical Society
2 Computers & Mathematics with Applications
2 Journal of Mathematical Physics
2 Mathematical Notes
2 Journal of Geometry and Physics
2 Acta Mathematica
2 Collectanea Mathematica
2 Journal of the Korean Mathematical Society
2 Journal of the London Mathematical Society. Second Series
2 Manuscripta Mathematica
2 Monatshefte für Mathematik
2 Pacific Journal of Mathematics
2 Proceedings of the Edinburgh Mathematical Society. Series II
2 Tôhoku Mathematical Journal. Second Series
2 Chinese Annals of Mathematics. Series B
2 Acta Mathematicae Applicatae Sinica. English Series
2 Journal of Integral Equations and Applications
2 The Journal of Geometric Analysis
2 Bulletin des Sciences Mathématiques
2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
2 Taiwanese Journal of Mathematics
2 Fractional Calculus & Applied Analysis
2 Communications in Nonlinear Science and Numerical Simulation
2 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms
2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
2 Proceedings of the Steklov Institute of Mathematics
2 Analysis & PDE
...and 78 more Serials

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