A population biological model with a singular nonlinearity.
type: Item
instance of: scholarly article
title: A population biological model with a singular nonlinearity.
zbMATH Open document ID: 1340.35056
author: S. H. Rasouli
published in: Applications of Mathematics
publication date: 2014-10-29T00:00:00Z
full work available at URL: http://hdl.handle.net/10338.dmlcz/143771
review text: The following quasilinear elliptic problem is considered \[ -{\text{div}}(|x|^{-\alpha p}|\nabla u|^{p-2}\nabla u)=|x|^{-(\alpha+1)p+\beta}\Big(au^{p-1}-f(u)-cu^{-\gamma} \Big) \] in a smooth and bounded domain \(\Omega\subset{\mathbb R}^N\) which contains the origin. Here \(1<p<N\), \(0\leq \alpha<(N-p)/p\), \(\gamma\in (0,1)\), and \(a,\alpha, \beta,c\) are positive constants. The solution is assumed to satisfy \(u=0\) on \(\partial\Omega\). Under some additional assumptions on \(f(u)\) and on the contants \(\gamma, a\) and \(c>0\) it is obtained the existence of a positive solution. The approach relies on the upper and lower solution method.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35B09
Mathematics Subject Classification ID: 35A01
zbMATH DE Number: 6362225
zbMATH Keywords: quasilinear elliptic problem
zbMATH Keywords: singularities
zbMATH Keywords: upper and lower solution method
zbMATH Keywords: population biology
Wikidata QID: Q113904510
MaRDI profile type: Publication
OpenAlex ID: W2027187949
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DOI: 10.1007/S10492-014-0053-7
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description: scientific article; zbMATH DE number 6362225