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Pseudo affine-periodic solutions for delay differential systems. (English) Zbl 1486.34135

The paper establishes sufficient conditions for existence and uniqueness of pseudo affine-periodic solutions of linear, semi-linear, as well as nonlinear differential equations with either bounded or unbounded delay. The main assumptions involve an exponential dichotomy property and pseudo affine-periodicity of the right-hand side. The proofs are based on fixed point arguments. The results are illustrated by two examples.

MSC:

34K13 Periodic solutions to functional-differential equations
34D09 Dichotomy, trichotomy of solutions to ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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