Existence results for nonlinear functional evolution equations with delay conditions
type: Item
instance of: scholarly article
title: Existence results for nonlinear functional evolution equations with delay conditions
zbMATH Open document ID: 1081.34078
author: Jong Soo Jung
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-02-22T00:00:00Z
review text: Let \(X\) be a real Banach space, \(A(t): D(A(t))\subset X\to 2^X\), \(G: [0,T]\times L^p((- r,0), X)\to X\). The following abstract nonlinear evolution equation with delay condition is considered \[ du(t)/dt+ A(t)u(t)\in G(t,u_t, L_t u),\;t\in [0,T],\;u(0)= \Phi_0(t)\text{ for }t\in [-r, 0].\tag{1} \] By using Schauder's fixed-point theorem in the space \(L^p((0, T),X)\), \(1\leq p\leq\infty\), a local existence theorem for the problem (1) is established. Here, it is assumed, among others, that the evolution operator \(U(t,s)\) generated by \(\{A(t)\}\) is equicontinuous.
reviewed by: Józef Banaś
Mathematics Subject Classification ID: 34K30
zbMATH DE Number: 2136803
zbMATH Keywords: Equicontinuity
zbMATH Keywords: \(m\)-Accretive operator
zbMATH Keywords: Evolution operator
zbMATH Keywords: Compact operator
zbMATH Keywords: Resolvent
MaRDI profile type: Publication
full work available at URL: j.na.2004.10.015
OpenAlex ID: W1965466832
cites work: Q4171189
cites work: Q5658694
cites work: On the Compactness of the Nonlinear Evolution Operator in a Banach Space
cites work: Compact Perturbations of m-Accretive Operators in General Banach Spaces
cites work: Local existence of integral solutions via compactness methods for nonlinear functional differential equations in \(L^p\) spaces
cites work: Existence of solutions of nonlinear functional integro-differential equations in Banach spaces
cites work: A compact evolution operator generated by a nonlinear time-dependent \(m\)-accretive operator in a Banach space
cites work: On the construction and the convergence of the method of lines for quasi-nonlinear functional evolutions in general banach spaces
cites work: Solvability of functional evolutions via compactness methods in general Banach spaces
cites work: Existence for nonlinear functional differential equations
cites work: Differential inclusions governed by non convex perturbations of \(m\)- accretive operators
cites work: Nonlinear evolution equations governed by f-quasi-dissipative operators
cites work: Nonlinear evolution operators and semigroups. Applications to partial differential equations
cites work: Differential equations associated with compact evolution generators
cites work: Compact evolution operators
cites work: Local existence theorems for nonlinear differential equations and compactness of integral solutions in Lp(0, T;X)
cites work: Compactness methods for an abstract nonlinear Volterra integrodifferential equation
cites work: Q4040177
DOI: 10.1016/J.NA.2004.10.015
description: scientific article; zbMATH DE number 2136803