Existence of solutions for quasilinear delay integrodifferential equations with nonlocal conditions (original) (raw)

New discussion on global existence and attractivity of mild solutions for nonautonomous integrodifferential equations with state-dependent delay

Electronic Journal of Mathematical Analysis and Applications

This paper investigates a functional integral differential equation with state-dependent delay in Banach spaces. This equation's linear part depends on time and generates a linear evolution system. Using the resolvent operator and fixed-point methods theory, we formulate a new set of sufficient conditions for mild solutions of functional integral-differential equations with state-dependent delays. The next part of this study examines the attractiveness of mild solutions for the system under consideration. Finally, we give an example to illustrate the theoretical results.

Existence of Solutions of Quasilinear Integrodifferential Equations with Nonlocal Condition

Tokyo Journal of Mathematics, 2000

We prove the existence and uniqueness of mild and classical solutions of a quasilinear integrodifferential equation with nonlocal condition. The results are obtained by using C0C_{0}C0-semigroup and the Banach fixed point theorem. 1. Introduction. The problem of existence of solutions of evolution equations with nonlocal conditions in Banach space has been studied first by Byszewski [8]. In that paper he has established the existence and uniqueness of mild, strong and classical solutions of the following nonIocal

Existence and regularity for some partial functional integrodifferential equations with infinite delay

2016

In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of the strict solution. The method used treats the equations in the domain of A with the graph norm employing results from linear semigroup theory. To illustrate our abstract result, we conclude this work with an application.

Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions

Abstract and Applied Analysis, 2012

Using Hausdorff measure of noncompactness and a fixed-point argument we prove the existence of mild solutions for the semilinear integrodifferential equation subject to nonlocal initial conditionsu′(t)=Au(t)+∫0tB(t-s)u(s)ds+f(t,u(t)),t∈[0,1],u(0)=g(u), whereA:D(A)⊆X→X, and for everyt∈[0,1]the mapsB(t):D(B(t))⊆X→Xare linear closed operators defined in a Banach spaceX. We assume further thatD(A)⊆D(B(t))for everyt∈[0,1], and the functionsf:[0,1]×X→Xandg:C([0,1];X)→XareX-valued functions which satisfy appropriate conditions.