The Non-Local Cauchy Problem for Semilinear Integrodifferential Equations With Deviating Argument

Abstract

The aim of this paper is to prove the existence and uniqueness of mild and classical solutions of the non-local Cauchy problem for a semilinear integrodifferential equation with deviating argument. The results are established by using the method of semigroups and the contraction mapping principle. The paper generalizes certain results of Lin and Liu.

A Class of Nonlocal Impulsive Problems for Integrodifferential Equations in Banach Spaces

“…For the importance of nonlocal conditions in different fields, we refer the reader to [7][8][9][10] and the references contained therein. Especially, the integrodifferential equations with nonlocal conditions has been investigated by Balachandran, Liu and other researchers extensively (see [11][12][13][14]17,18,21]). …”

Existence of solutions of Sobolev‐type semilinear mixed integrodifferential inclusions in Banach spaces

“…Several authors have studied the nonlocal Cauchy problem in abstract spaces [2,3,4,11,12,13]. The importance of nonlocal conditions is discussed in [4,5].…”

“…The problem of proving the existence of mild solutions for differential and integrodifferential equations in abstract spaces has been studied by several authors [2,4,11,12,13]. Balachandran and Uchiyama [3] established the existence of solutions of nonlinear integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces.…”

Existence Results on General Integrodifferential Evolution Equations in Banach Space

“…The nonlocal Cauchy problem for the same equation has been studied by Byszewskii [2,3]. Balachandran and Chandrasekaran [4] investigated the nonlocal Cauchy problem for semilinear integrodifferential equation with deviating argument.…”