Sign-changing solutions to singular second-order boundary value problems.
type: Item
instance of: scholarly article
title: Sign-changing solutions to singular second-order boundary value problems.
zbMATH Open document ID: 1142.35428
author: P. Joseph Mckenna
author: W. Reichel
published in: Advances in Differential Equations
publication date: 2002-02-04T00:00:00Z
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 35B15
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1700788
zbMATH Keywords: singular BVP
zbMATH Keywords: sign-changing solutions
zbMATH Keywords: boundary behaviour
MaRDI profile type: Publication
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review text: The authors' present an general framework for sign-changing solutions of NEWLINE\[NEWLINEu''+ p(x)|u|^{-\gamma}= 0\quad\text{on }(a,b)\tag{1}NEWLINE\]NEWLINE and its multidimensional analogue NEWLINE\[NEWLINE\begin{gathered} \Delta u+ p(x) u^{(-\gamma)}= 0\quad\text{in }\Omega,\\ u= 0\quad\text{on }\partial\Omega\end{gathered}\tag{2}NEWLINE\]NEWLINE on a bounded, smooth domain \(\Omega\subset\mathbb{R}^N\). Here \(s^{(-\gamma)}\) stands for the odd power-function \(|s|^{-\gamma}\) signs. To this end the authors use erlatiely prcise determination of the boundary behaviour of positive solution of (2). Sign-changing principal-value solutions are constructed by gluing together solutions of one sign.
description: scientific article; zbMATH DE number 1700788