Existence of solutions to a class of partial functional integrodifferential equations with nonlocal conditions
type: Item
instance of: scholarly article
zbMATH Open document ID: 1280.34075
author: Zuomao Yan
publication date: 2012-09-11T00:00:00Z
full work available at URL: index.html
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 6081074
zbMATH Keywords: partial functional integrodifferential equations
zbMATH Keywords: fixed point
zbMATH Keywords: nonlocal condition
zbMATH Keywords: resolvent operator
MaRDI profile type: Publication
Recommended article: Existence of solutions for some functional integrodifferential equations with nonlocal conditions
Recommended article: Existence results for some partial integrodifferential equations with nonlocal conditions
Recommended article: Existence and Regularity of Solutions for Some Partial Integrodifferential Equations Involving the Nonlocal Conditions
Recommended article: Existence of solutions for nonlinear functional integrodifferential evolution equations with nonlocal conditions
Recommended article: Q5474514
Recommended article: Q3397084
Recommended article: Existence of solutions of nonlinear integrodifferential equation with nonlocal condition
Recommended article: Existence of a mild solution of a functional integrodifferential equation with nonlocal condition
Recommended article: Local existence and global continuation for some partial functional integrodifferential equations
Recommended article: Existence of solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal conditions
title: Existence of solutions to a class of partial functional integrodifferential equations with nonlocal conditions
published in: International Journal of Mathematical Analysis (Ruse)
review text: The aim of this work is to prove the existence of mild solutions for some integrodifferential equations with nonlocal conditions. The linear part is assumed to have a resolvent operator in the sense provided by Grimmer, the nonlinear part is assumed to be continuous or Lipschitz. The resolvent operator plays a crucial role in that paper, since it helps to get a variation of constant formula for the mild solutions. The author gives enough conditions ensuring the existence of the resolvent operators and then uses this formula and many fixed point theorems to show the existence of the mild solution, like Banach's fixed point theorem or the Leary-Schauder alternative. Banach's fixed point theorem is applied when a Lipschitz condition is assumed. The compactness of the resolvent operator is used when the Leary-Schauder alternative is applied.
reviewed by: Khalil Ezzinbi
description: scientific article; zbMATH DE number 6081074