Search

In this paper, we consider recurrent behavior of bounded solutions for a functional integro-differential equation arising from heat conduction in materials with memory. Prior to the main results, we give a new version of composite theorem on measure pseudo almost automorphic functions involved in delay. Based on recently obtained results on the uniform exponential stability as well as contraction mapping principle, we prove some existence and uniqueness theorems on the recurrence of bounded mild solutions for the addressed equations with infinite delay. Finally, we finish this paper with an example on partial integro-differential equation which frequently comes to light in the study of heat conduction. Keywords and phrases: almost automorphy, bounded solutions, integro-differential equations, infinite delay. AMS Subject Classification: 34K14, 43A60, 45N05, 45D05, 1. Introduction. Let u = u(x, t) denote the temperature at position x [member of] [??] and time t, (where [??] is a bounded subset of [??]) and the heat [...]

This paper is mainly concerned with the existence and uniqueness of solutions for fractional integrodifferential equations with interval impulses and infinite delay. The results are obtained by using Schauder's fixed point theorem. An example illustrating our main result is given. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with the existence of mild solutions for a first-order impulsive neutral integro-differential equation with state-dependent delay. We assume that the undelayed part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed-point theorem for condensing maps combined with theories of analytic resolvent operators, we prove some existence theorems. As an application of these main theorems, some practical consequences are derived. [ABSTRACT FROM AUTHOR]

In this paper, the controllability of second-order differential and integrodifferential inclusions in Banach spaces are investigated. Two new results are obtained by using the theory of strongly continuous cosine families and a fixed-point theorem for multivalued maps. [ABSTRACT FROM AUTHOR]