Fredholm operators, evolution semigroups, and periodic solutions of nonlinear periodic systems

DOI10.1016/j.jde.2014.08.007zbMath1305.34089OpenAlexW2073931924MaRDI QIDQ743896

Toshiki Naito, Jong Son Shin, Dohan Kim, Rinko Miyazaki

Publication date: 1 October 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2014.08.007

zbMATH Keywords

decompositionperiodic solutionFredholm operatorevolution semigroupnonlinear periodic systemnormal eigenvalue

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) One-parameter semigroups and linear evolution equations (47D06) Nonlinear differential equations in abstract spaces (34G20) Spectrum, resolvent (47A10) (Semi-) Fredholm operators; index theories (47A53)

Related Items (6)

Dichotomy and periodic solutions to partial functional differential equations ⋮ SOLUTIONS OF HIGHER ORDER INHOMOGENEOUS PERIODIC EVOLUTIONARY PROCESS ⋮ Affine‐periodic orbits for linear dynamical systems ⋮ Generalized eigenspaces of generators of evolution semigroups ⋮ Almost periodic solutions of periodic second order linear evolution equations ⋮ Almost Periodic Solutions of Periodic Linear Partial Functional Differential Equations

Cites Work

• On the spectral theory of elliptic differential operators. I
• A modified Poincaré method for the persistence of periodic orbits and applications
• Circular spectrum and bounded solutions of periodic evolution equations
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• Evolution semigroups and spectral criteria for almost periodic solutions of periodic evolution equations
• Periodic motions
• Perturbation theory for linear operators.
• Representations of solutions, translation formulae and asymptotic behavior in discrete linear systems and periodic continuous linear systems
• Existence and Stability for Partial Functional Differential Equations
• Periodic solutions for evolution equations
• Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems
• Analytic semigroups and optimal regularity in parabolic problems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Fredholm operators, evolution semigroups, and periodic solutions of nonlinear periodic systems