Local attractivity for integro-differential equations with noncompact semigroups

Abstract

In this paper, we are devoted to study the existence and local attractivity of solutions for a class of integro-differential equations.Under the situation that the nonlinear term satisfy Carathéodory conditions and a noncompactness measure condition, we establish some existence and local attractivity of mild solutions by utilizing Mönch fixed point theorem, Kuratowski measure of noncompactness and resolvent operator theory in the sense of Grimmer.Our investigations will be situated in the Banach space of real functions which are defined, continuous, and bounded on the right-hand real half axis 𝕉+. Moreover an example is given to illustrate our outcomes.

Functional Integro-Differential Equations with State-Dependent Delay and Non-Instantaneous Impulsions: Existence and Qualitative Results

“…As in [29,43], for some r > r > 1, we assume that Γ(ϑ) ≤ e − rϑ r , and Γ (ϑ) ≤ e − rϑ r 2 , we get that R(ϑ) ≤ e − σϑ , where σ = 1 − r −1 .…”