Existence and localization of solution for second order elliptic BVP in presence of lower and upper solutions without any order
type: Item
instance of: scholarly article
title: Existence and localization of solution for second order elliptic BVP in presence of lower and upper solutions without any order
zbMATH Open document ID: 0908.35042
author: C. De Coster
author: Marc Henrard
published in: Journal of Differential Equations
publication date: 1999-02-07T00:00:00Z
review text: It is proved an existence and localization result for a solution of a second order semilinear elliptic problem of the type \[ Lu(x)=f(x,u(x),\nabla u(x))\quad\text{ in }\Omega,\quad u|_{\partial\Omega \setminus\Gamma}=0,\quad Bu=d\zeta \quad \text{on }\Gamma. \] The main result is obtained assuming the existence of a lower and an upper solution without particular order and a positively homogeneous asymptotic behavior of the right hand member of the equation. In the final section a similar result is proved for a \(p\)-Laplacian boundary value problem.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 1206627
zbMATH Keywords: degree
zbMATH Keywords: multiplicity
zbMATH Keywords: \(p\)-Laplacian
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3423
OpenAlex ID: W1979965911
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DOI: 10.1006/JDEQ.1998.3423
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description: scientific article; zbMATH DE number 1206627