The averaging principle and periodic solutions for nonlinear evolution equations at resonance

DOI10.1016/j.na.2013.02.030zbMath1292.34059arXiv1505.00158OpenAlexW2963132351MaRDI QIDQ387151

Piotr Kokocki

Publication date: 19 December 2013

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.00158

zbMATH Keywords

evolution equationtopological degreespectral decompositionfractional power spaceheat equation, periodic solutionresonanse, sectorial operator, semigroups of operatorstranslation along trajectories operator

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear differential equations in abstract spaces (34G20) Averaging method for ordinary differential equations (34C29) Applications of operator theory to differential and integral equations (47N20)

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Cites Work

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• Periodic solutions of damped hyperbolic equations at resonance: a translation along trajectories approach.
• Periodic solutions of nonlinear hyperbolic evolution systems
• Periodic solutions for nonlinear evolution equations at resonance
• A continuation principle for forced oscillations on differentiable manifolds
• Krasnosel'skii type formula and translation along trajectories method for evolution equations
• Geometric theory of semilinear parabolic equations
• A note on bounded solutions of second-order differential equations at resonance
• Topological degree methods for perturbations of operators generating compact \(C_0\) semigroups
• Nonlinear elliptic boundary value problems at resonance
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• Unique continuation for elliptic operators: A geometric-variational approach
• On bounded nonlinear perturbations of an elliptic equation at resonance
• Strict Monotonicity of Eigenvalues and Unique Continuation
• Resonance and non-resonance in a problem of boundedness