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Butler, Geoffrey J.

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Author ID: butler.geoffrey-j Recent zbMATH articles by "Butler, Geoffrey J."
Published as: Butler, G. J.; Butler, G.; Butler, Geoffrey J.; Butler, Geoffrey
External Links: MGP
Documents Indexed: 68 Publications since 1970
Biographic References: 13 Publications

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Citations contained in zbMATH Open

51 Publications have been cited 1,080 times in 814 Documents Cited by Year
Uniformly persistent systems. Zbl 0603.34043
Butler, Geoffrey; Freedman, H. I.; Waltman, Paul
222
1986
Persistence in dynamical systems. Zbl 0603.58033
Butler, Geoffrey; Waltman, Paul
147
1986
A mathematical model of the chemostat with a general class of functions describing nutrient uptake. Zbl 0569.92020
Butler, G. J.; Wolkowicz, G. S. K.
97
1985
A mathematical model of the chemostat with periodic washout rate. Zbl 0584.92027
Butler, G. J.; Hsu, S. B.; Waltman, Paul
97
1985
Riccati techniques and variational principles in oscillation theory for linear systems. Zbl 0648.34031
Butler, G. J.; Erbe, L. H.; Mingarelli, A. B.
59
1987
Integral averages and the oscillations of second order ordinary differential equations. Zbl 0424.34033
Butler, G. J.
41
1980
Coexistence of competing predators in a chemostat. Zbl 0508.92019
Butler, G. J.; Hsu, S. B.; Waltman, P.
37
1983
Bifurcation from a limit cycle in a two predator-one prey ecosystem modeled on a chemostat. Zbl 0475.92017
Butler, G. J.; Waltman, Paul
36
1981
Rapid oscillation, non-extendability and the existence of periodic solutions to second order nonlinear ordinary differential equations. Zbl 0299.34050
Butler, G. J.
29
1976
Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources. Zbl 0609.92035
Butler, G. J.; Wolkowicz, G. S. K.
28
1987
Predator-mediated competition in the chemostat. Zbl 0604.92019
Butler, G. J.; Wolkowicz, G. S. K.
22
1986
Oscillation theorems for a nonlinear analogue of Hill’s equation. Zbl 0341.34018
Butler, G. J.
21
1976
Oscillation results for second order differential systems. Zbl 0583.34027
Butler, G. J.; Erbe, L. H.
21
1986
Oscillation results for selfadjoint differential systems. Zbl 0588.34025
Butler, G. J.; Erbe, L. H.
18
1986
On the oscillatory behaviour of a second order nonlinear differential equation. Zbl 0307.34029
Butler, G. J.
17
1975
Periodic solutions of a predator-prey system with periodic coefficients. Zbl 0471.92020
Butler, G. J.; Freedman, H. I.
15
1981
The oscillatory behavior of a second order nonlinear differential equation with damping. Zbl 0348.34022
Butler, G. J.
15
1977
Abelian group unification algorithms for elementary terms. Zbl 0555.68065
Lankford, D.; Butler, G.; Brady, B.
11
1984
A generalization of a lemma of Bihari and applications to pointwise estimates for integral equations. Zbl 0209.42503
Butler, Geoffrey; Rogers, T.
11
1971
Simultaneous packing and covering in Euclidean space. Zbl 0251.52022
Butler, G. J.
11
1972
Periodic points and chaotic functions in the unit interval. Zbl 0389.54026
Butler, G. J.; Pianigiani, G.
11
1978
Global dynamics of a selection model for the growth of a population with genotypic fertility differences. Zbl 0499.92017
Butler, G. J.; Freedman, H. I.; Waltman, Paul
10
1982
Hille-Wintner type comparison theorems for second-order ordinary differential equations. Zbl 0415.34032
Butler, G. J.
10
1979
The existence of continuable solutions of a second order differential equation. Zbl 0346.34004
Butler, G. J.
8
1977
Nonnegative solutions of a quadratic matrix equation arising from comparison theorems in ordinary differential equations. Zbl 0558.15005
Butler, G. J.; Johnson, Charles R.; Wolkowicz, H.
7
1985
Periodic solutions of sublinear second order differential equations. Zbl 0402.34028
Butler, G. J.
7
1978
A generalization of Olech-Opial-Wazewski oscillation criteria to second order nonlinear equations. Zbl 0617.34028
Butler, G. J.; Erbe, L. H.
6
1987
Integral comparison theorems and extremal points for linear differential equations. Zbl 0528.34037
Butler, G. J.; Erbe, L. H.
6
1983
Predator - mediated coexistence in a chemostat: Coexistence and competition reversal. Zbl 0621.92020
Butler, G. J.; Wolkowicz, G. S. K.
5
1987
Nonlinear integral Riccati systems and comparison theorems for linear differential equations. Zbl 0534.34036
Butler, G. J.; Erbe, L. H.
5
1983
Limiting the complexity of limit sets in self-regulating systems. Zbl 0707.92001
Butler, Geoffrey; Schmid, Rudolf; Waltman, Paul
5
1990
Almost all 1-set contractions have a fixed point. Zbl 0411.47034
Butler, G. J.
5
1979
A general backtrack algorithm for the isomorphism problem of combinatorial objects. Zbl 0611.05030
Butler, G.; Lam, C. W. H.
4
1985
An \(L^ p\) saturation theorem for splines. Zbl 0229.41005
Butler, G. J.; Richards, F. B.
4
1972
Oscillation theory for second order differential systems with functionally commutative matrix coefficients. Zbl 0613.34025
Butler, G. J.; Erbe, L. H.
3
1985
An integral criterion for the oscillation of a second order sublinear ordinary differential equation. Zbl 0532.34024
Butler, G. J.
3
1982
Competitive predator-prey systems and coexistence. Zbl 0532.92026
Butler, G. J.
3
1983
Further critical cases of the scalar implicit function theorem. Zbl 0247.26011
Butler, G. J.; Freedman, H. I.
3
1972
A progress report on new decision algorithms for finitely presented abelian groups. Zbl 0547.03009
Lankford, D.; Butler, G.; Ballantyne, A.
3
1984
Coexistence in predator-prey systems. Zbl 0435.92024
Butler, G. J.
3
1980
Some properties of second order linear differential equations and perturbations that preserve them. Zbl 0559.34056
Butler, G. J.; Rao, V. Sree Hari
2
1984
The Poincaré-Birkhoff ”twist” theorem and periodic solutions of second- order nonlinear differential equations. Zbl 0588.34032
Butler, G. J.
2
1980
Persistence in dynamical systems models of three-population ecological communities. Zbl 0623.92025
Butler, G. J.; Freedman, H. I.; Waltman, P.
2
1987
The rank theorem for locally Lipschitz continuous functions. Zbl 0608.58007
Butler, G. J.; Timourian, J. G.; Viger, C.
1
1988
Persistence in three-dimensional Lotka-Volterra systems. Zbl 0632.92019
Butler, G. J.; Waltman, P.
1
1988
Comparison theorems for second-order operator-valued linear differential equations. Zbl 0546.34028
Butler, G. J.; Erbe, L. H.
1
1984
An extremal property of simplices. Zbl 0222.52009
Butler, G. J.
1
1971
Oscillation and comparison theorems for second order linear differential equations with integrable coefficients. Zbl 0279.34023
Butler, G.; Macki, J. W.
1
1974
The existence of continuable solutions of a second order differential equation. Zbl 0332.34003
Butler, G. J.
1
1977
The existence of continuable solutions of a second order differential equation: Erratum. Zbl 0399.34005
Butler, G. J.
1
1979
The genericity of the convergence of successive approximations in Banach spaces. Zbl 0449.34045
Butler, G. J.
1
1979
Limiting the complexity of limit sets in self-regulating systems. Zbl 0707.92001
Butler, Geoffrey; Schmid, Rudolf; Waltman, Paul
5
1990
The rank theorem for locally Lipschitz continuous functions. Zbl 0608.58007
Butler, G. J.; Timourian, J. G.; Viger, C.
1
1988
Persistence in three-dimensional Lotka-Volterra systems. Zbl 0632.92019
Butler, G. J.; Waltman, P.
1
1988
Riccati techniques and variational principles in oscillation theory for linear systems. Zbl 0648.34031
Butler, G. J.; Erbe, L. H.; Mingarelli, A. B.
59
1987
Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources. Zbl 0609.92035
Butler, G. J.; Wolkowicz, G. S. K.
28
1987
A generalization of Olech-Opial-Wazewski oscillation criteria to second order nonlinear equations. Zbl 0617.34028
Butler, G. J.; Erbe, L. H.
6
1987
Predator - mediated coexistence in a chemostat: Coexistence and competition reversal. Zbl 0621.92020
Butler, G. J.; Wolkowicz, G. S. K.
5
1987
Persistence in dynamical systems models of three-population ecological communities. Zbl 0623.92025
Butler, G. J.; Freedman, H. I.; Waltman, P.
2
1987
Uniformly persistent systems. Zbl 0603.34043
Butler, Geoffrey; Freedman, H. I.; Waltman, Paul
222
1986
Persistence in dynamical systems. Zbl 0603.58033
Butler, Geoffrey; Waltman, Paul
147
1986
Predator-mediated competition in the chemostat. Zbl 0604.92019
Butler, G. J.; Wolkowicz, G. S. K.
22
1986
Oscillation results for second order differential systems. Zbl 0583.34027
Butler, G. J.; Erbe, L. H.
21
1986
Oscillation results for selfadjoint differential systems. Zbl 0588.34025
Butler, G. J.; Erbe, L. H.
18
1986
A mathematical model of the chemostat with a general class of functions describing nutrient uptake. Zbl 0569.92020
Butler, G. J.; Wolkowicz, G. S. K.
97
1985
A mathematical model of the chemostat with periodic washout rate. Zbl 0584.92027
Butler, G. J.; Hsu, S. B.; Waltman, Paul
97
1985
Nonnegative solutions of a quadratic matrix equation arising from comparison theorems in ordinary differential equations. Zbl 0558.15005
Butler, G. J.; Johnson, Charles R.; Wolkowicz, H.
7
1985
A general backtrack algorithm for the isomorphism problem of combinatorial objects. Zbl 0611.05030
Butler, G.; Lam, C. W. H.
4
1985
Oscillation theory for second order differential systems with functionally commutative matrix coefficients. Zbl 0613.34025
Butler, G. J.; Erbe, L. H.
3
1985
Abelian group unification algorithms for elementary terms. Zbl 0555.68065
Lankford, D.; Butler, G.; Brady, B.
11
1984
A progress report on new decision algorithms for finitely presented abelian groups. Zbl 0547.03009
Lankford, D.; Butler, G.; Ballantyne, A.
3
1984
Some properties of second order linear differential equations and perturbations that preserve them. Zbl 0559.34056
Butler, G. J.; Rao, V. Sree Hari
2
1984
Comparison theorems for second-order operator-valued linear differential equations. Zbl 0546.34028
Butler, G. J.; Erbe, L. H.
1
1984
Coexistence of competing predators in a chemostat. Zbl 0508.92019
Butler, G. J.; Hsu, S. B.; Waltman, P.
37
1983
Integral comparison theorems and extremal points for linear differential equations. Zbl 0528.34037
Butler, G. J.; Erbe, L. H.
6
1983
Nonlinear integral Riccati systems and comparison theorems for linear differential equations. Zbl 0534.34036
Butler, G. J.; Erbe, L. H.
5
1983
Competitive predator-prey systems and coexistence. Zbl 0532.92026
Butler, G. J.
3
1983
Global dynamics of a selection model for the growth of a population with genotypic fertility differences. Zbl 0499.92017
Butler, G. J.; Freedman, H. I.; Waltman, Paul
10
1982
An integral criterion for the oscillation of a second order sublinear ordinary differential equation. Zbl 0532.34024
Butler, G. J.
3
1982
Bifurcation from a limit cycle in a two predator-one prey ecosystem modeled on a chemostat. Zbl 0475.92017
Butler, G. J.; Waltman, Paul
36
1981
Periodic solutions of a predator-prey system with periodic coefficients. Zbl 0471.92020
Butler, G. J.; Freedman, H. I.
15
1981
Integral averages and the oscillations of second order ordinary differential equations. Zbl 0424.34033
Butler, G. J.
41
1980
Coexistence in predator-prey systems. Zbl 0435.92024
Butler, G. J.
3
1980
The Poincaré-Birkhoff ”twist” theorem and periodic solutions of second- order nonlinear differential equations. Zbl 0588.34032
Butler, G. J.
2
1980
Hille-Wintner type comparison theorems for second-order ordinary differential equations. Zbl 0415.34032
Butler, G. J.
10
1979
Almost all 1-set contractions have a fixed point. Zbl 0411.47034
Butler, G. J.
5
1979
The existence of continuable solutions of a second order differential equation: Erratum. Zbl 0399.34005
Butler, G. J.
1
1979
The genericity of the convergence of successive approximations in Banach spaces. Zbl 0449.34045
Butler, G. J.
1
1979
Periodic points and chaotic functions in the unit interval. Zbl 0389.54026
Butler, G. J.; Pianigiani, G.
11
1978
Periodic solutions of sublinear second order differential equations. Zbl 0402.34028
Butler, G. J.
7
1978
The oscillatory behavior of a second order nonlinear differential equation with damping. Zbl 0348.34022
Butler, G. J.
15
1977
The existence of continuable solutions of a second order differential equation. Zbl 0346.34004
Butler, G. J.
8
1977
The existence of continuable solutions of a second order differential equation. Zbl 0332.34003
Butler, G. J.
1
1977
Rapid oscillation, non-extendability and the existence of periodic solutions to second order nonlinear ordinary differential equations. Zbl 0299.34050
Butler, G. J.
29
1976
Oscillation theorems for a nonlinear analogue of Hill’s equation. Zbl 0341.34018
Butler, G. J.
21
1976
On the oscillatory behaviour of a second order nonlinear differential equation. Zbl 0307.34029
Butler, G. J.
17
1975
Oscillation and comparison theorems for second order linear differential equations with integrable coefficients. Zbl 0279.34023
Butler, G.; Macki, J. W.
1
1974
Simultaneous packing and covering in Euclidean space. Zbl 0251.52022
Butler, G. J.
11
1972
An \(L^ p\) saturation theorem for splines. Zbl 0229.41005
Butler, G. J.; Richards, F. B.
4
1972
Further critical cases of the scalar implicit function theorem. Zbl 0247.26011
Butler, G. J.; Freedman, H. I.
3
1972
A generalization of a lemma of Bihari and applications to pointwise estimates for integral equations. Zbl 0209.42503
Butler, Geoffrey; Rogers, T.
11
1971
An extremal property of simplices. Zbl 0222.52009
Butler, G. J.
1
1971
all top 5

Cited by 909 Authors

27 Freedman, Herbert Irving
21 Chen, Lansun
20 Wolkowicz, Gail S. K.
19 Meng, Fanwei
17 Wang, Yuanshi
16 Zanolin, Fabio
15 Butler, Geoffrey J.
13 Erbe, Lynn Harry
13 Sun, Yuangong
13 Takeuchi, Yasuhiro
12 Waltman, Paul Elvis
12 Yuan, Sanling
11 Jang, Sophia R.-J.
11 Pang, Guoping
11 Wong, James S. W.
10 Wang, Fengyan
9 Song, Xinyu
9 Teng, Zhi-dong
8 Ruan, Shigui
8 Samanta, Guru Prasad
8 Schreiber, Sebastian J.
8 Yang, Qigui
8 Zheng, Zhaowen
7 Boscaggin, Alberto
7 Hsu, Szebi
7 Jiang, Daqing
7 Ma, Wanbiao
7 Meng, Xinzhu
7 Pavlou, Stavros
7 Rapaport, Alain
7 Shi, Xiangyun
7 Smith, Hal Leslie
7 Wu, Hong
7 Zhang, Tonghua
6 Cui, Jingan
6 Li, Wan-Tong
6 Mukherjee, Debasis
6 Peterson, Allan C.
6 Pilyugin, Sergei S.
6 Rao, Vadrevu Sree Hari
6 So, Joseph Wai-Hung
5 Baglama, James
5 Cushing, Jim M.
5 Hofbauer, Josef
5 Kuang, Yang
5 Li, Bingtuan
5 Li, Michael Yi
5 Li, Zuxiong
5 Naito, Manabu
5 Pal, Samaresh
5 Philos, Christos G.
5 Sari, Tewfik
5 Sikder, Asim
5 Zhao, Xiao-Qiang
5 Zhou, Xueyong
4 Agarwal, Ravi P.
4 Ahmad, Shair
4 Ballyk, Mary M.
4 Bhattacharyya, Joydeb
4 Braselton, James P.
4 Braselton, Lorraine M.
4 Cai, Shaohong
4 Dambrosio, Walter
4 Das, Krishnapada
4 Feltrin, Guglielmo
4 Hadeler, Karl-Peter
4 Han, Maoan
4 Jiang, Jifa
4 Jiao, Jianjun
4 Kirane, Mokhtar
4 Kong, Qingkai
4 Kwong, Man Kam
4 Liu, Haidong
4 Lu, Zhengyi
4 Maiti, Alakes
4 Mao, Xuerong
4 Mathsen, Ronald M.
4 Ozair, Muhammad
4 Rai, Bindhyachal
4 Rehim, Mehbuba
4 Rogovchenko, Yuri V.
4 Roy, Amiya Bhusan
4 Sanjurjo, José M. R.
4 Sharma, Swarnali
4 Sun, Shulin
4 Tang, Betty K. P.
4 Tatar, Nasser-eddine
4 Tiryaki, Aydin
4 Vayenas, D. V.
4 Wang, Liang
4 Wang, Lin
4 Wang, Qiru
4 Wu, Jianhua
4 Xu, Chaoqun
4 Yang, Yu
4 Zhang, Shuwen
4 Zhao, Zhong
3 Abell, Martha L.
3 Baltzis, Basil C.
3 Chattopadhyay, Joydev
...and 809 more Authors
all top 5

Cited in 136 Serials

85 Journal of Mathematical Analysis and Applications
62 Mathematical Biosciences
56 Applied Mathematics and Computation
41 Journal of Mathematical Biology
41 Journal of Differential Equations
25 Chaos, Solitons and Fractals
23 Rocky Mountain Journal of Mathematics
21 Bulletin of Mathematical Biology
21 Proceedings of the American Mathematical Society
21 Journal of Mathematical Chemistry
17 Nonlinear Analysis. Real World Applications
17 Nonlinear Analysis. Theory, Methods & Applications
16 Mathematical and Computer Modelling
14 Computers & Mathematics with Applications
13 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
13 Journal of Biological Dynamics
12 Differential Equations and Dynamical Systems
12 Discrete Dynamics in Nature and Society
11 Theoretical Population Biology
11 Discrete and Continuous Dynamical Systems. Series B
10 Communications in Nonlinear Science and Numerical Simulation
10 Journal of Theoretical Biology
9 Applied Mathematics Letters
9 Applied Mathematical Modelling
9 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
9 Journal of Biological Systems
8 Mathematical Methods in the Applied Sciences
8 Annali di Matematica Pura ed Applicata. Serie Quarta
8 Transactions of the American Mathematical Society
8 Journal of Applied Mathematics and Computing
8 Advances in Difference Equations
8 International Journal of Biomathematics
6 Journal of Computational and Applied Mathematics
6 Nonlinear Dynamics
6 Abstract and Applied Analysis
5 Journal of Dynamics and Differential Equations
4 Archiv der Mathematik
4 Acta Applicandae Mathematicae
4 Linear Algebra and its Applications
4 Journal of Applied Mathematics
4 Journal of Applied Analysis and Computation
3 Czechoslovak Mathematical Journal
3 Results in Mathematics
3 Aequationes Mathematicae
3 SIAM Journal on Applied Mathematics
3 Journal of Difference Equations and Applications
3 Discrete and Continuous Dynamical Systems
3 Advanced Nonlinear Studies
3 Nonlinear Analysis. Hybrid Systems
2 Applicable Analysis
2 Archive for Rational Mechanics and Analysis
2 Ukrainian Mathematical Journal
2 Advances in Mathematics
2 Rendiconti del Seminario Matematico della Università di Padova
2 Tohoku Mathematical Journal. Second Series
2 Systems & Control Letters
2 Zeitschrift für Analysis und ihre Anwendungen
2 Physica D
2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
2 Stochastic Processes and their Applications
2 Applied Mathematics. Series B (English Edition)
2 Journal of Inequalities and Applications
2 Chaos
2 Natural Resource Modeling
2 Acta Mathematica Sinica. English Series
2 The ANZIAM Journal
2 Dynamical Systems
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Mathematical Biosciences and Engineering
2 Mathematical Modelling of Natural Phenomena
2 International Journal of Differential Equations
2 Afrika Matematika
2 ISRN Applied Mathematics
1 Bulletin of the Australian Mathematical Society
1 Discrete Applied Mathematics
1 Discrete Mathematics
1 Mathematical Notes
1 Nonlinearity
1 Physica A
1 Reports on Mathematical Physics
1 Archivum Mathematicum
1 Canadian Mathematical Bulletin
1 Inventiones Mathematicae
1 Journal of Approximation Theory
1 Journal of Combinatorial Theory. Series A
1 Journal of Functional Analysis
1 Journal of Soviet Mathematics
1 Manuscripta Mathematica
1 Mathematics and Computers in Simulation
1 Mathematische Zeitschrift
1 Monatshefte für Mathematik
1 Numerische Mathematik
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
1 Topology and its Applications
1 Statistics & Probability Letters
1 SIAM Journal on Algebraic and Discrete Methods
1 Applied Mathematics and Mechanics. (English Edition)
1 Bulletin of the Iranian Mathematical Society
1 Statistics
1 Discrete & Computational Geometry
...and 36 more Serials

Citations by Year