Existence Results for a Second Order Impulsive Neutral Functional Integrodierential Inclusions in Banach Spaces with Innite Delay

Abstract

A fixed point theorem for condensing maps due to Martelli combined with theories of a strongly continuous cosine family of bounded linear operators is used to investigate the existence of solutions to second order impulsive neutral functional integrodifferential inclusions with infinite delay in Banach spaces.Keywords: Second order impulsive integrodifferential inclusion, cosine functions of operators, mild solution, Martelli's fixed point theorem.

Approximate Controllability of Neutral Differential Systems with Fractional Deformable Derivatives

“…Further investigation started with a discussion of previously published works [10,[27][28][29]. Specifically, the existence and uniqueness of the mild solutions and approximate controllability of fractional evolution equations with deformable derivatives were investigated in [29,30]…”

Fixed points of multivalued maps under local Lipschitz conditions and applications

“…For this reason, last years several researchers have studied various aspects of the theory. We mention here [1,2,6,8,12,13,20,21,24,26,29] and references in these works for the motivations of the theory.…”

Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions

“…For this reason this topic has attracted the attention of many authors in the last time. We only mention here the papers [7][8][9][10][11][12][13][14][15][16][17] which are directly related with the objective of this paper.…”

“…On the other hand, it is well known that retarded functional differential equations are used to model important concrete phenomena. For general aspects of the theory of partial differential equations with delay we refer to [27], and for functional differential inclusions we refer to [7,9,[12][13][14]28]. In similar way, there exists an extensive literature concerning abstract second order problems.…”