Sufficient conditions for existence of solutions of nonlinear differential equations with nonlocal boundary conditions
type: Item
instance of: scholarly article
title: Sufficient conditions for existence of solutions of nonlinear differential equations with nonlocal boundary conditions
zbMATH Open document ID: 1283.34013
author: Kristen Kobylus Abernathy
publication date: 2013-11-05T00:00:00Z
full work available at URL: dea-05-21.pdf
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6222678
zbMATH Keywords: boundary value problems
zbMATH Keywords: Schauder fixed point theorem
zbMATH Keywords: existence
MaRDI profile type: Publication
OpenAlex ID: W2330800528
DOI: 10.7153/DEA-05-21
published in: Differential Equations and Applications
review text: The authors consider the boundary value problems NEWLINE\[NEWLINEy^{(n)}(t)+ \dots +a_1(t)y'(t)+a_0(t)y(t)=f(y(t),y'(t))+\varepsilon G(y,\dots,y^{(n-1)})(t),NEWLINE\]NEWLINE NEWLINE\[NEWLINE\sum_{j=1}^nb_{ij}(0)y^{(j-1)}(0)+\sum_{j=1}^nb_{ij}(t_1)y^{(j-1)}(t_1) +\dots+\sum_{j=1}^nb_{ij}(t_N)y^{(j-1)}(t_N)=0\text{ for }i=1,2,\dots,n.NEWLINE\]NEWLINE They provide easily verifiable sufficient conditions for the existence of solutions. These conditions are based on the solution space of the corresponding linear, homogeneous problem and on the size of the nonlinear perturbation. The main results are more general than those in [\textit{J. Rodríguez}, Int. J. Pure Appl. Math. 54, No. 2, 215--226 (2009; Zbl 1184.34029)].
reviewed by: Ruyun Ma
description: scientific article; zbMATH DE number 6222678