Abstract existence theorems of positive solutions for nonlinear boundary value problems
type: Item
instance of: scholarly article
title: Abstract existence theorems of positive solutions for nonlinear boundary value problems
zbMATH Open document ID: 1064.47058
author: Yongxiang Li
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-09-23T00:00:00Z
review text: The present paper deals with the existence of positive solutions to the operator equation \[ Lu=f(x,u),\qquad u\in D(L), \] where \(\Omega\subset {\mathbb R}^n\) is a bounded domain, \(H=L^2(\Omega),\) \(L: L(D)\subset H\to H\) is an unbounded linear operator and \(f: \overline\Omega\times {\mathbb R}\to {\mathbb R}^+\) is a continuous function. The author proposes conditions on \(L\) and \(f\) which ensure the existence of positive solutions to the equation considered. The discussion is based on the Krasnoselskii fixed point theorem of cone mapping and the fixed point index in cones. The abstract theory is applied to some ordinary differential equations (Sturm-Liouville problem, periodic problems for ODEs), extending and improving known results.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 47H07
Mathematics Subject Classification ID: 34L30
zbMATH DE Number: 2102568
zbMATH Keywords: abstract boundary value problem
zbMATH Keywords: unbounded linear operator
zbMATH Keywords: \(e\)-positive solution
zbMATH Keywords: cone
zbMATH Keywords: fixed point index
MaRDI profile type: Publication
full work available at URL: j.na.2004.02.010
OpenAlex ID: W2095258059
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DOI: 10.1016/J.NA.2004.02.010
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description: scientific article; zbMATH DE number 2102568