Boundary blow-up solutions for a class of elliptic equations on a bounded domain
type: Item
instance of: scholarly article
title: Boundary blow-up solutions for a class of elliptic equations on a bounded domain
zbMATH Open document ID: 1186.35079
author: Angelo Roncalli
author: José Valdo A. Gonçalves
published in: Applied Mathematics and Computation
publication date: 2007-01-09T00:00:00Z
review text: This paper deals with existence of solutions of the quasilinear elliptic equation \[ \Delta u=f(x,u,\nabla u) \] in \(\Omega\) satisfying the boundary blow-up condition \(u(x)\to\infty\) as \({x\to\partial\Omega}\), where \(\Omega\subset\mathbb R^ N\) is a bounded domain with smooth boundary \(\partial\Omega\). Our main result applies to the existence of blow-up solutions of a class of equations which appear in Stochastic Control Theory, namely \[ \Delta u=a(x)g(u)+\lambda| \nabla u| ^ \sigma+\Psi(x) \] in \(\Omega\), where \(a(x)\), \(g(u)\), \(\Psi(x)\) are suitable functions and \(\lambda\), \(\sigma\) are nonnegative constants. Our approach employs an approximation procedure combined with both a non-monotone iteration variant of the method of lower and upper solutions and fixed point arguments.
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 5083659
zbMATH Keywords: quasilinear elliptic problem
zbMATH Keywords: bounded domain
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: boundary blow-up
MaRDI profile type: Publication
full work available at URL: j.amc.2006.03.029
OpenAlex ID: W2084200117
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DOI: 10.1016/J.AMC.2006.03.029
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description: scientific article; zbMATH DE number 5083659