Existence and asymptotic periodicity of solutions for neutral integro-differential evolution equations with infinite delay

Authors

  • Jianbo Zhu East China Normal University
  • Xianlong Fu East China Normal University

DOI:

https://doi.org/10.1515/ms-2022-0009

Keywords:

Neutral integro-differential evolution equation, asymptotic periodicity, infinite delay, resolvent operator

Abstract

In this work, making use of the theory of resolvent operators and Banach fixed point theorem, we first discuss the existence and regularity of mild solutions for neutral partial functional integro-differential equations with infinite delay. We assume that the linear part of the considered equation generates a resolvent operator and the nonlinear function satisfies Lipschitz conditions. Then we investigate the asymptotic periodicity of mild solutions under asymptotic periodic assumption on the nonlinear function. The obtained results extend somewhat the related conclusions in literature. In the end, an example is presented to illustrate the obtained results.

Author Biographies

Jianbo Zhu, East China Normal University

School of Mathematical Sciences
Shanghai Key Laboratory of PMMP
East China Normal University
Shanghai 200241
P. R. CHINA

Xianlong Fu, East China Normal University

School of Mathematical Sciences
Shanghai Key Laboratory of PMMP
East China Normal University
Shanghai 200241
P. R. CHINA

Published

2022-02-16

Issue

Section

Articles - Other topics