Existence of compact support solutions for a quasilinear and singular problem.
type: Item
instance of: scholarly article
title: Existence of compact support solutions for a quasilinear and singular problem.
zbMATH Open document ID: 1265.35059
author: Jacques Giacomoni
author: Paul Sauvy
author: Habib Mâagli
published in: Differential and Integral Equations
publication date: 2012-10-08T00:00:00Z
review text: This paper deals with the quasilinear problem in a bounded smooth domain \(\Omega \) involving the \(p\)-Laplacian. The nonlinearity is of the form \(K(x)(\lambda u^q - u^r),\) where \( -1<r<q<p-1\), \(K\) is a positive function having the singular behavior near the boundary of \(\Omega \) and \(\lambda \) is a parameter. The singularity of \(K\) behaves as a negative power of the distance from the boundary. Besides non-existence results for \(\lambda \) small, the authors prove also the existence of positive or compact support (positive) solutions for \(\lambda \) large, depending on the assumptions on parameters \(p, q\) and \(r\). This work extends similar results for semilinear problem \((p=2)\) due to \textit{Y. Haitao} [J. Math. Anal. Appl. 319, No. 2, 830--840 (2006; Zbl 1155.35363)].
reviewed by: Pavel Drábek
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 6092264
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: singular problem
zbMATH Keywords: existence of positive solutions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6092264