Abstract
In this paper, we show the existence of mild solutions to a nonlocal problem of impulsive integrodifferential equations via a measure of noncompactness in a Banach space. Our work is based on a new fixed point theorem and it generalizes some existing results on the topic in the sense that we do not require the semigroup and nonlinearity involved in the problem to be compact.
Highlights
1 Introduction In this paper, we discuss the existence of solutions for the following nonlocal problem of integrodifferential equations: du(t) = Au(t) + f t, u(t), Gu(t), dt t ∈ [, K], t = ti, u( ) = u + g(u), ( . )
The theory of semigroups of bounded linear operators is closely related to the solution of differential and integrodifferential equations in Banach spaces
In a recent paper [ ], the authors studied the existence of mild solutions to an impulsive differential equation with nonlocal conditions by applying Darbo-Sadovskii’s fixed point theorem
Summary
1 Introduction In this paper, we discuss the existence of solutions for the following nonlocal problem of integrodifferential equations: du(t) = Au(t) + f t, u(t), Gu(t) , dt t ∈ [ , K], t = ti, u( ) = u + g(u), The theory of semigroups of bounded linear operators is closely related to the solution of differential and integrodifferential equations in Banach spaces.
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