Solvability of the \(\varPhi \)-Laplacian with nonlocal boundary conditions
type: Item
instance of: scholarly article
title: Solvability of the \(\varPhi \)-Laplacian with nonlocal boundary conditions
zbMATH Open document ID: 1195.34034
author: George Karakostas
published in: Applied Mathematics and Computation
publication date: 2009-10-09T00:00:00Z
review text: Sufficient conditions are obtained for the existence of at least one positive solution to a nonlinear boundary value problem with nonlocal linear boundary conditions \[ [\Phi(x'(t))]'+ c(t)(Fx)(t)= 0,\qquad t\in (0,1), \] \[ x(0)- L_0(x)= x(1)- L_1(x)= 0, \] where \(\Phi\) is an increasing homeomorphism of the real lline onto itself, \(F\) is a nonlinear operator, \(L_0\), \(L_1\) are bounded linear positive operators. The proof is based on the fixed-point theorem in cones by Krasnoselskii. Some examples are given.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5612828
zbMATH Keywords: Krasnoselskii's fixed point theorem
zbMATH Keywords: \(\varPhi \)-Laplacian operator equation
zbMATH Keywords: positive solutions
zbMATH Keywords: boundary value problems
reviewed by: Sergei A. Brykalov
MaRDI profile type: Publication
full work available at URL: j.amc.2009.05.022
OpenAlex ID: W2082066286
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DOI: 10.1016/J.AMC.2009.05.022
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description: scientific article; zbMATH DE number 5612828