Further remarks on the non-degeneracy condition
type: Item
instance of: scholarly article
title: Further remarks on the non-degeneracy condition
zbMATH Open document ID: 1073.35088
DOI: 10.1007/BF03323383
author: Philip Korman
published in: Results in Mathematics
publication date: 2004-11-26T00:00:00Z
review text: The author considers positive solutions of the semilinear boundary value problem \[ \Delta u(x)+\lambda f(u(x))= 0\quad \text{in }\Omega,\qquad u= 0\quad \text{on }\partial\Omega, \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^n\), whose boundary is of class \(C^2\), \(f\in C^1(\overline{\mathbb{R}}_+)\) and \(\lambda> 0\). In contrast to the previous results in this direction (the structure of the set of positive solutions) the author did not assume that \(\Omega\) is either symmetric or convex.
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 2119247
zbMATH Keywords: positive solution
zbMATH Keywords: semilinear elliptic problem
zbMATH Keywords: symmetric domain
zbMATH Keywords: non-convex domain
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2119247