Existence of solutions to nonlinear differential equations with nonlocal conditions
type: Item
instance of: scholarly article
title: Existence of solutions to nonlinear differential equations with nonlocal conditions
zbMATH Open document ID: 0971.34045
author: Mouffak Benchohra
author: Sotiris K. Ntouyas
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-10-30T00:00:00Z
review text: The authors consider the initial value problem for an abstract nonlinear ordinary differential equation of first order in some Banach space. The initial condition, which is a nonlocal condition, is of the type \(y(0)+ g(y)=y_0\), where \(g\) is some continuous function. Using a classical fixed-point theorem for compact maps due to Schäfer, the authors prove the existence of mild solutions.
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1563472
zbMATH Keywords: nonlinear evolution equation
zbMATH Keywords: nonlocal condition
zbMATH Keywords: mild solution
zbMATH Keywords: fixed-point theorem
reviewed by: Etienne Emmrich
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7106
OpenAlex ID: W2092004434
cites work: Nonlinear problems for systems of differential equations
cites work: Existence and uniqueness of mild and strong solutions of a semilinear evolution equation with nonlocal conditions
cites work: Existence of solutions of a delay differential equation with nonlocal condition
cites work: Q4890144
cites work: Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem
cites work: Q5533443
cites work: Nonzero solutions of nonlinear systems of differential equations via fixed point theorems for multivalued maps
cites work: Q5580482
cites work: Nonzero solutions of boundary value problems for nonlinear systems
cites work: Q3209464
cites work: Global existence for semilinear evolution equations with nonlocal conditions
cites work: Über die Methode der a priori-Schranken
cites work: Q4051163
DOI: 10.1006/JMAA.2000.7106
description: scientific article; zbMATH DE number 1563472