Positive solutions of singular Dirichlet and periodic boundary value problems
type: Item
instance of: scholarly article
title: Positive solutions of singular Dirichlet and periodic boundary value problems
zbMATH Open document ID: 1008.34012
DOI: 10.1016/S0898-1221(01)00313-3
author: Svatoslav Staněk
publication date: 2002-08-15T00:00:00Z
review text: Consider the equation \[ (r(x)x')'= \mu q(t) f(t,x(t)) \] where \(t \in J:=[0,T]\), \(q(t)>0\) in \(J\), \(r(x)>0\) on \((0,A]\) may be singular at \(x=0\), \(f(t,x)\leq 0\) on \(J\times (0,A)\) may be singular at \(x=0\) and \(x=A\). Sufficient conditions for the existence of solutions \(x\) with \(0<x<A\) in \((0,T)\), satisfying the Dirichlet boundary conditions \(x(0)=x(T)=0\), as well as for the existence of solutions satisfying also the periodic conditions \(x(0)=x'(0)=x(T)=x'(T)=0\), are established.
reviewed by: Cristina Marcelli
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1781529
zbMATH Keywords: Dirichlet problems
zbMATH Keywords: periodic problems
zbMATH Keywords: singular problems
zbMATH Keywords: positive solutions
MaRDI profile type: Publication
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full work available at URL: s0898-1221(01)00313-3
OpenAlex ID: W2169574282
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1781529