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Found 100 Documents (Results 1–100)

On asymptotics of the spectrum of an integral operator with a logarithmic kernel of a special form. (English. Russian original) Zbl 07810127

Differ. Equ. 59, No. 12, 1721-1733 (2023); translation from Differ. Uravn. 59, No. 12, 1680-1691 (2023).
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Singularly perturbed integro-differential systems with kernels depending on solutions of differential equations. (English. Russian original) Zbl 1522.45005

Differ. Equ. 59, No. 5, 707-719 (2023); translation from Differ. Uravn. 59, No. 5, 693-704 (2023).
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On the solvability of a system of nonlinear integral equations with the Hammerstein-Stieltjes operator on the half-line. (English. Russian original) Zbl 1518.45006

Differ. Equ. 59, No. 3, 383-391 (2023); translation from Differ. Uravn. 59, No. 3, 380-388 (2023).
MSC:  45G15 45M05
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Asymptotics of the solution of a singularly perturbed system of equations with a single-scale internal layer. (English. Russian original) Zbl 1523.34060

Differ. Equ. 59, No. 3, 332-350 (2023); translation from Differ. Uravn. 59, No. 3, 333-349 (2023).
MSC:  34E15 34B15 34E05
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Uniform convergence of spectral expansions for a problem with a boundary condition depending on a spectral parameter. (English. Russian original) Zbl 1510.34040

Differ. Equ. 58, No. 9, 1153-1174 (2022); translation from Differ. Uravn. 58, No. 9, 1165-1185 (2022).
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On one class of multidimensional integral equations of convolution type with convex nonlinearity. (English. Russian original) Zbl 1496.45010

Differ. Equ. 58, No. 5, 680-690 (2022); translation from Differ. Uravn. 58, No. 5, 686-695 (2022).
MSC:  45K05 45M05
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On the asymptotics of the nonreal spectrum of the integro-differential Gurtin-Pipkin equation with relaxation kernels representable in the form of the Stielties integral. (English. Russian original) Zbl 1490.45013

Differ. Equ. 58, No. 2, 242-255 (2022); translation from Differ. Uravn. 58, No. 2, 238-251 (2022).
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Nonlinear Volterra equations with loads and bifurcation parameters: existence theorems and construction of solutions. (English. Russian original) Zbl 1486.45003

Differ. Equ. 57, No. 12, 1640-1651 (2021); translation from Differ. Uravn. 57, No. 12, 1654-1664 (2021).
MSC:  45D05 45M05 37G10
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Existence of periodic solutions of a third-order nonlinear system. (English. Russian original) Zbl 1485.34134

Differ. Equ. 57, No. 10, 1341-1357 (2021); translation from Differ. Uravn. 57, No. 10, 1367-1383 (2021).
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On positive bounded solutions of one class of nonlinear integral equations with the Hammerstein-Nemytskii operator. (English. Russian original) Zbl 1469.45013

Differ. Equ. 57, No. 6, 768-779 (2021); translation from Differ. Uravn. 57, No. 6, 784-795 (2021).
MSC:  45M20 45M05
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Regularized asymptotic solutions of nonlinear integro-differential equations with zero operator in the differential part and with several rapidly varying kernels. (English. Russian original) Zbl 1469.45010

Differ. Equ. 57, No. 6, 753-767 (2021); translation from Differ. Uravn. 57, No. 6, 769-783 (2021).
MSC:  45M05 45G10 65R20
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Regularized asymptotics of solutions of integro-differential equations with zero operator in the differential part and with slowly and rapidly varying kernels. (English. Russian original) Zbl 1465.45007

Differ. Equ. 56, No. 4, 523-532 (2020); translation from Differ. Uravn. 56, No. 4, 534-543 (2020).
MSC:  45J05 45M05
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Bifurcation of the equilibrium of an oscillator with a velocity-dependent restoring force under periodic perturbations. (English. Russian original) Zbl 1437.34048

Differ. Equ. 55, No. 8, 1011-1016 (2019); translation from Differ. Uravn. 55, No. 8, 1045-1050 (2019).
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Bifurcation of an oscillatory mode under a periodic perturbation of a special oscillator. (English. Russian original) Zbl 1428.34052

Differ. Equ. 55, No. 6, 753-757 (2019); translation from Differ. Uravn. 55, No. 6, 769-773 (2019).
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Distribution of the spectrum of a singular Sturm-Liouville operator perturbed by the Dirac delta function. (English. Russian original) Zbl 1419.34233

Differ. Equ. 55, No. 2, 169-180 (2019); translation from Differ. Uravn. 55, No. 2, 168-179 (2019).
MSC:  34L15 34L40 34E10
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On the asymptotics of eigenvalues of a fourth-order differential operator with matrix coefficients. (English. Russian original) Zbl 1395.34085

Differ. Equ. 54, No. 4, 450-467 (2018); translation from Differ. Uravn. 54, No. 4, 458-474 (2018).
MSC:  34L20 34B09
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Construction of asymptotics of solutions of differential equations with cusp-type degeneration in the coefficients in the case of multiple roots of the highest-order symbol. (English. Russian original) Zbl 1402.34056

Differ. Equ. 54, No. 1, 28-37 (2018); translation from Differ. Uravn. 54, No. 1, 30-39 (2018).
MSC:  34D05 34A30
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Quasiperiodic perturbations of two-dimensional Hamiltonian systems. (English. Russian original) Zbl 1394.34088

Differ. Equ. 53, No. 12, 1557-1566 (2017); translation from Differ. Uravn. 53, No. 12, 1607-1615 (2017).
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Theory of bifurcations of the Schrödinger equation. (English. Russian original) Zbl 1385.34045

Differ. Equ. 53, No. 7, 855-863 (2017); translation from Differ. Uravn. 53, No. 7, 882-890 (2017).
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Step-like contrast structure for a nonlinear system of singularly perturbed differential equations in the critical case. (English) Zbl 1361.34068

Differ. Equ. 52, No. 12, 1575-1584 (2016); translation from Differ. Uravn. 52, No. 12, 1647-1656 (2016).
MSC:  34E05 34E15 34B15
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Passage to the limit in a singularly perturbed partial integro-differential system. (English. Russian original) Zbl 1359.45004

Differ. Equ. 52, No. 9, 1115-1122 (2016); translation from Differ. Uravn. 52, No. 9, 1160-1167 (2016).
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Periodic perturbations of a nonlinear oscillator. (English. Russian original) Zbl 1355.34092

Differ. Equ. 52, No. 4, 405-412 (2016); translation from Differ. Uravn. 52, No. 4, 411-418 (2016).
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Properties of the spectrum in the John problem on a freely floating submerged body in a finite basin. (English. Russian original) Zbl 1294.35110

Differ. Equ. 49, No. 12, 1544-1559 (2013); translation from Differ. Uravn. 49, No. 12, 1591-1606 (2013).
MSC:  35Q35 76B15 35P20
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Asymptotic solution of a singularly perturbed optimal control problem related to the reconstruction of a defective curve. (English. Russian original) Zbl 1298.49004

Differ. Equ. 49, No. 11, 1347-1355 (2013); translation from Differ. Uravn. 49, No. 11, 1381-1389 (2013).
MSC:  49J15
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Asymptotic formulas for fundamental solutions of the Dirac system with complex-valued integrable potential. (English. Russian original) Zbl 1283.34078

Differ. Equ. 49, No. 5, 545-556 (2013); translation from Differ. Uravn. 49, No. 5, 573-584 (2013).
MSC:  34L40 34L10 34D05
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On the asymptotic behavior of solutions of integro-differential equations in a Hilbert space. (English. Russian original) Zbl 1279.45014

Differ. Equ. 49, No. 6, 718-730 (2013); translation from Differ. Uravn. 49, No. 6, 746-758 (2013).
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Limit cycles under perturbations of a quadratic Hamiltonian system. (English. Russian original) Zbl 1283.34029

Differ. Equ. 48, No. 5, 693-700 (2012); translation from Differ. Uravn. 48, No. 5, 686-693 (2012).
MSC:  34C07 34C25 34E10
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Averaging principle and a variational approach to the problem of bifurcation of periodic solutions from nonisolated equilibria of the averaged equation. (English. Russian original) Zbl 1264.34089

Differ. Equ. 48, No. 3, 328-335 (2012); translation from Differ. Uravn. 48, No. 3, 326-333 (2012).
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Asymptotic behavior of the solution of a system of nonlinear integro-differential equations. (English. Russian original) Zbl 1243.45012

Differ. Equ. 48, No. 1, 72-80 (2012); translation from Differ. Uravn. 48, No. 1, 70-78 (2012).
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On a class of two-dimensional adjoint integral equations of Volterra type. (English. Russian original) Zbl 1237.45001

Differ. Equ. 47, No. 9, 1333-1343 (2011); translation from Differ. Uravn. 47, No. 9, 1320-1330 (2011).
MSC:  45E05 45D05 45M05
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On the asymptotics of the optimal value of the performance functional in a linear optimal control problem. (English. Russian original) Zbl 1230.49037

Differ. Equ. 47, No. 4, 560-570 (2011); translation from Differ. Uravn. 47, No. 4, 560-570 (2011).
MSC:  49N60 93C05 34H05 49M30
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Asymptotic analysis of singularly perturbed integro-differential equations with zero operator in the differential part. (English. Russian original) Zbl 1235.45006

Differ. Equ. 47, No. 4, 516-533 (2011); translation from Differ. Uravn. 47, No. 4, 516-533 (2011).
MSC:  45J05 45M05
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How to estimate the number of limit cycles in Liénard systems with a small parameter. (English. Russian original) Zbl 1270.34051

Differ. Equ. 47, No. 2, 224-230 (2011); translation from Differ. Uravn. 47, No. 2, 225-230 (2011).
MSC:  34C07 34C05 34E10
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Asymptotic behavior of the spectrum of a convolution operator on a finite interval with the transform of the integral kernel being a characteristic function. (English. Russian original) Zbl 1211.45011

Differ. Equ. 46, No. 10, 1519-1523 (2010); translation from Differ. Uravn. 46, No. 10, 1516-1520 (2010).
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Differential equations with degeneration and resurgent analysis. (English. Russian original) Zbl 1221.34153

Differ. Equ. 46, No. 9, 1267-1286 (2010); translation from Differ. Uravn. 46, No. 9, 1259-1277 (2010).
MSC:  34E05 34M30
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Asymptotic expansion of the solution of the first boundary value problem for the Schrödinger system near conical points of the boundary. (English. Russian original) Zbl 1197.35078

Differ. Equ. 46, No. 2, 289-293 (2010); translation from Differ. Uravn. 46, No. 2, 285-289 (2010).
MSC:  35C20 35G46
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Regularized asymptotics of solutions of systems of Fredholm integro-differential equations with rapidly varying kernels. (English. Russian original) Zbl 1177.45008

Differ. Equ. 45, No. 2, 226-239 (2009); translation from Differ. Uravn. 45, No. 2, 220-233 (2009).
Reviewer: Li Xing (Yinchuan)
MSC:  45M05 45J05 45L05
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On the spectral instability of the Sturm-Liouville operator with a complex potential. (English. Russian original) Zbl 1188.47037

Differ. Equ. 45, No. 4, 494-509 (2009); translation from Differ. Uravn. 45, No. 4, 480-495 (2009).
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On the stabilization of solutions of an initial-boundary value problem for a nonlinear integro-differential equation. (English. Russian original) Zbl 1136.78018

Differ. Equ. 43, No. 6, 854-861 (2007); translation from Differ. Uravn. 43, No. 6, 833-840 (2007).
MSC:  78M35 45M05 78A25
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An application of a nonlinear integral equation for finding the asymptotics of a solution of a nonlinear heat equation. (English. Russian original) Zbl 1130.45005

Differ. Equ. 43, No. 1, 96-107 (2007); translation from Differ. Uravn. 43, No. 1, 90-100 (2007).
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A criterion for the asymptotic stability of singular differential systems by the linear diagonal approximation. (English. Russian original) Zbl 1157.34331

Differ. Equ. 42, No. 8, 1095-1101 (2006); translation from Differ. Uravn. 42, No. 8, 1035-1040 (2006).
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On the asymptotics of solutions of nonlinear second-order differential equations. (English. Russian original) Zbl 1139.34039

Differ. Equ. 41, No. 8, 1105-1114 (2005); translation from Differ. Uravn. 41, No. 8, 1053-1061 (2005).
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On the asymptotics of the solution of the Cauchy problem for some differential-difference parabolic equations. (English. Russian original) Zbl 1088.35075

Differ. Equ. 41, No. 4, 570-581 (2005); translation from Differ. Uravn. 41, No. 4, 538-548 (2005).
MSC:  35R10 35B40 35K15
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A periodic singularly perturbed problem for the matrix Riccati equation. (English. Russian original) Zbl 1094.34037

Differ. Equ. 41, No. 4, 529-537 (2005); translation from Differ. Uravn. 41, No. 4, 500-507 (2005).
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Nonpreservation of asymptotic properties of solutions of singular linear differential systems under small perturbations. (English. Russian original) Zbl 1090.34573

Differ. Equ. 41, No. 2, 213-218 (2005); translation from Differ. Uravn. 41, No. 2, 202-207 (2005).
MSC:  34E10 34A30 34D10
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Asymptotic methods for solving the Hamilton equations by the parametrization of canonical transformations. (English. Russian original) Zbl 1077.37041

Differ. Equ. 40, No. 5, 672-685 (2004); translation from Differ. Uravn. 40, No. 5, 626-638 (2004).
MSC:  37J45 34E10 70H05
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Asymptotic behavior of the density of the spectral measure of the singular Sturm-Liouville operator. (English. Russian original) Zbl 1093.34011

Differ. Equ. 40, No. 4, 524-541 (2004); translation from Differ. Uravn. 40, No. 4, 485-499 (2004).
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On a small stabilizing perturbation of a singular differential equation with a constant operator and a degenerate coefficient of the general form. (English. Russian original) Zbl 1076.34064

Differ. Equ. 40, No. 2, 190-198 (2004); translation from Differ. Uravn. 40, No. 2, 183-190 (2004).
MSC:  34G10 47D06 34E10
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Singularly perturbed integro-differential equations with diagonal degeneration of the kernel in reverse time. (English. Russian original) Zbl 1072.45006

Differ. Equ. 40, No. 1, 120-127 (2004); translation from Differ. Uravn. 40, No. 1, 112-119 (2004).
MSC:  45J05 45M05 45L05
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Exponential asymptotics of the solution of the second boundary value problem for a second-order parabolic equation with a small parameter. (English. Russian original) Zbl 1065.35033

Differ. Equ. 39, No. 6, 853-864 (2003); translation from Differ. Uravn. 39, No. 6, 809-819 (2003).
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The spectral asymptotics of a quadratic pencil of differential operators. (English. Russian original) Zbl 1079.47047

Differ. Equ. 39, No. 8, 1117-1123 (2003); translation from Differ. Uravn. 39, No. 8, 1062-1067 (2003).
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The asymptotics of eigenvalues and eigenfunctions of a singular quasidifferential operator on a finite interval. (English. Russian original) Zbl 1078.34533

Differ. Equ. 39, No. 8, 1098-1105 (2003); translation from Differ. Uravn. 39, No. 8, 1044-1051 (2003).
MSC:  34L20 47E05
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The asymptotics of eigenvalues and eigenfunctions and a trace formula for a potential with Delta functions. (English. Russian original) Zbl 1043.34092

Differ. Equ. 38, No. 6, 772-789 (2002); translation from Differ. Uravn. 38, No. 6, 735-751 (2002).
MSC:  34L20 34B05
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Regularized asymptotic solutions of singularly perturbed integral systems with a diagonal degeneration of the kernel. (English. Russian original) Zbl 1025.45006

Differ. Equ. 37, No. 10, 1399-1411 (2001); translation from Differ. Uravn. 37, No. 10, 1330-1341 (2001).
MSC:  45M05 45F15 45L05
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The exponential asymptotics of solutions of the Kolmogorov-Feller equation. (English. Russian original) Zbl 1020.35127

Differ. Equ. 37, No. 9, 1340-1344 (2001); translation from Differ. Uravn. 37, No. 9, 1273-1276 (2001).
MSC:  35R60 35B40 35A08
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On an integral representation of resurgent functions. (English. Russian original) Zbl 1065.30023

Differ. Equ. 37, No. 9, 1291-1302 (2001); translation from Differ. Uravn. 37, No. 9, 1229-1238 (2001).
MSC:  30D15 30E15 34M37 34Exx 34M30
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A step-like contrast structure for the case of a multiple root of the transition point equation (the critical case). (English. Russian original) Zbl 1013.34056

Differ. Equ. 37, No. 2, 185-194 (2001); translation from Differ. Uravn. 37, No. 2, 171-180 (2001).
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The asymptotic method of differential inequalities for singularly perturbed integro-differential equations. (English. Russian original) Zbl 0991.45004

Differ. Equ. 36, No. 10, 1544-1551 (2000); translation from Differ. Uravn. 36, No. 10, 1398-1404 (2000).
MSC:  45J05 45G10 45M05
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Homogenization of boundary value problems in domains with rapidly oscillating nonperiodic boundary. (English. Russian original) Zbl 0993.35013

Differ. Equ. 36, No. 6, 833-846 (2000); translation from Differ. Uravn. 36, No. 6, 754-764 (2000).
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An asymptotic method of differential inequalities for the investigation of periodic contrast structures: Existence, asymptotics, and stability. (English. Russian original) Zbl 0979.35150

Differ. Equ. 36, No. 2, 298-305 (2000); translation from Differ. Uravn. 36, No. 2, 262-269 (2000).
MSC:  35R45 35K57 35B40 35A05
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