On positive solutions of some singularly perturbed problems where the nonlinearity changes sign
type: Item
instance of: scholarly article
title: On positive solutions of some singularly perturbed problems where the nonlinearity changes sign
zbMATH Open document ID: 0835.35013
DOI: 10.12775/TMNA.1995.009
published in: Topological Methods in Nonlinear Analysis
publication date: 1996-04-25T00:00:00Z
review text: The existence of positive solutions of the Dirichlet problem \[ - \varepsilon \Delta u= g(u) \quad \text{in }D,\qquad u= 0 \quad \text{on } \partial D\tag{1} \] is studied. Here, \(D\) is a bounded domain in \(\mathbb{R}^n\) and \(g\) is \(C^1\)-function. Under various assumptions on \(D\) and \(g\) the author finds the exact number of positive solutions to (1). The results in this paper improve considerably analogous results of the author [Rocky Mt. J. Math. (to appear)].
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 807919
zbMATH Keywords: exact number of positive solutions
author: E. N. Dancer
MaRDI profile type: Publication
full work available at URL: tmna.1995.009
OpenAlex ID: W2585725993
description: scientific article; zbMATH DE number 807919