Pseudo–almost‐periodic solutions for delayed differential equations with integrable dichotomies and bi–almost‐periodic Green functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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