On the integro‐differential equations with reflection

Integrodifferential Equations with Analytic Semigroups

In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.

Integrodifferential Equations with Non-autonomous Operators

The result of Da Prato and Sinestrari [3] concerning the non-autonomous evolution operators of hyperbolic type for the equation u′(t) = A(t)u(t) + f(t), t ∈ [0, T ], w(0) = w0, is applied to the study of u′(t) = A(t) [ u(t)+ ∫ t −∞ G(t, s)u(s)ds ] +K(t)u(t)+f(t), t ∈ [0, T ], u(s) = φ(s), s ≤ 0, which models linear viscoelasticity. Here A(·) satisfies all the requirements of Kato’s semigroup ap...

Nonlinear Neutral Integrodifferential Equations on Unbounded Intervals

Abstract In this paper we prove the existence of solutions for a boundary value nonlinear neutral integrodifferential problem in Rn defined on an unbounded interval. The result is obtained by using the Schaefer fixed point theorem and by using a recent result [4] on compactness of a continuous operator K : BC(I,Rn) → BC(I,Rn); here BC(I,Rn) is the Banach space of continuous functions from the (...

Impulsive integrodifferential Equations and Measure of noncompactness

This paper is concerned with the existence of mild solutions for impulsive integro-differential equations with nonlocal conditions. We apply the technique measure of noncompactness in the space of piecewise continuous functions and by using Darbo-Sadovskii's fixed point theorem, we prove reasults about impulsive integro-differential equations for convex-power condensing operators.

On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space