Global existence of solutions to some semilinear integro-differential evolution equations with sign-varying kernels

Kun-Peng Jin,Jin Liang,Ti-Jun Xiao

doi:10.1515/msds-2020-0109

Abstract

AbstractIn this paper, we study the global existence of solutions to some semilinear integro-differential evolution equations in Hilbert spaces with sign-varying kernels. By treating the problem through fixed point theory and energy method, we obtain the global existence theorem on [0, +∞) of mild and strong solution to the evolution equations with memory effects for oscillating and sign-varying kernels. This theorem generalizes and improves some previous existence results.

Highlights

In this paper, we study the global existence of solutions to some semilinear integro-di erential evolution equations in Hilbert spaces with sign-varying kernels
The basic properties of variuos integral or integral di erential equations, including the existence and uniqueness of local or global solutions, the boundedness of solutions, the stability of solutions, the periodicity of solutions, etc., have always been important research topics concerned by researchers, and a large number of monographs and papers on these topics have been published, i.e, relevant studies have achieved fruitful results
Stimulated by Corduneanu’s signi cant works as well as other related works

Summary

Introduction

The basic properties of variuos integral or integral di erential equations, including the existence and uniqueness of local or global solutions, the boundedness of solutions, the stability of solutions, the periodicity of solutions, etc., have always been important research topics concerned by researchers, and a large number of monographs and papers on these topics have been published, i.e, relevant studies have achieved fruitful results. Abstract: In this paper, we study the global existence of solutions to some semilinear integro-di erential evolution equations in Hilbert spaces with sign-varying kernels. By treating the problem through xed point theory and energy method, we obtain the global existence theorem on [ , +∞) of mild and strong solution to the evolution equations with memory e ects for oscillating and sign-varying kernels.

Results

Conclusion