Existence principles and theory for singular Dirichlet boundary value problems
type: Item
instance of: scholarly article
title: Existence principles and theory for singular Dirichlet boundary value problems
zbMATH Open document ID: 0876.34018
author: Donal O'Regan
published in: Differential Equations and Dynamical Systems
publication date: 1997-11-25T00:00:00Z
review text: The singular boundary value problem \[ y''+q(t) g(t,y)=0, \qquad 0<t<1, \qquad y(0)=a, \qquad y(1)=b,\tag{1} \] where \(q\in C(0,1)\), \(q>0\) on \((0,1)\), \(\int_0^1 t(1-t)q(t)dt<\infty\), \(g\in C([0,1]\times \mathbb{R})\) is solved using the lower and upper solutions. Problem (1) is solved also in the case when \(g\) has a singularity at \(y=0\) and \(a=b=0\). Then a sequence of modified problems is solved and by means of the Arzela-Ascoli theorem the searched solution is established.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1014373
zbMATH Keywords: generalized Emden-Fowler equation
zbMATH Keywords: singular boundary value problem
zbMATH Keywords: lower and upper solutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1014373