A decomposition theorem for bounded solutions and the existence of periodic solutions to periodic differential equations

DOI10.1006/jdeq.1999.3673zbMath0948.34034OpenAlexW2029725063MaRDI QIDQ1969983

Rinko Miyazaki, Jong Son Shin, Toshiki Naito, Nguyen Van Minh

Publication date: 1 May 2000

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

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3673

zbMATH Keywords

periodic solutionFourier coefficientsdecomposition theoremperiodic evolution equationabstract functional-differential equationspectrum of bounded function

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear differential equations in abstract spaces (34G20)

Related Items (16)

Boundedness and almost periodicity of solutions of partial functional differential equations ⋮ A Massera theorem for asymptotic periodic solutions of periodic evolution equations ⋮ Pseudo almost periodic solutions to some non-autonomous neutral functional differential equations with unbounded delay ⋮ On the almost automorphy of bounded solutions of differential equations with piecewise constant argument ⋮ Existence and global asymptotical stability of periodic solution for the \(T\)-periodic logistic system with time-varying generating operators and \(T_{0}\)-periodic impulsive perturbations on Banach spaces ⋮ Periodic solutions and attractiveness for some partial functional differential equations with lack of compactness ⋮ Linear impulsive periodic system with time-varying generating operators on Banach space ⋮ Massera criterion for abstract functional differential equations with advance and delay ⋮ Existence of periodic solutions in abstract semilinear equations and applications to biological models ⋮ Boundedness and almost periodicity in dynamical systems ⋮ Massera criterion for periodic solutions of differential equations with piecewise constant argu\-ment ⋮ A Massera type theorem for almost automorphic solutions of differential equations ⋮ Almost Periodic Solutions of Periodic Linear Partial Functional Differential Equations ⋮ Evolution semigroups and sums of commuting operators: A new approach to the admissibility theory of function spaces ⋮ On Massera and Bohr-Neugebauer type theorems for some almost automorphic differential equations ⋮ A Katznelson-Tzafriri type theorem for difference equations and applications

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