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Pseudo–almost‐periodic solutions for delayed differential equations with integrable dichotomies and bi–almost‐periodic Green functions
Authors:Manuel Pinto  Claudio Vidal
Affiliation:1. Departamento de Matemática, Facultad de Ciencias, Universidad de Chile, Santiago, Chile;2. Grupo de Investigación en Sistemas Dinámicos y Aplicaciones (GISDA), Departamento de Matemática, Facultad de Ciencias, Universidad del Bío‐Bío, Concepción, VIII Región, Chile
Abstract:Using the existence of integrable bi–almost‐periodic Green functions of linear homogeneous differential equations and the contraction fixed point, we are able to prove the existence of almost and pseudo–almost‐periodic mild solutions under quite general hypotheses for the differential equation with constant delay in a Banach space X, where τ>0 is a fixed constant. The results extend the corresponding ones in the case of exponential dichotomy. Some examples illustrate the importance of the concepts.
Keywords:almost‐periodic solutions  functional differential equations  integrable dichotomy  pseudo–  almost‐periodic solutions  some examples illustrate the importance of the concepts
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