Exact multiplicity for some quasilinear elliptic Dirichlet problems where the non-linearity changes sign
type: Item
instance of: scholarly article
title: Exact multiplicity for some quasilinear elliptic Dirichlet problems where the non-linearity changes sign
zbMATH Open document ID: 1073.35047
author: Zongming Guo
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-06-01T00:00:00Z
review text: The author establishes the existence of one positive radially symmetric solutions \(u\) of \[ \Delta_pu + af(u) = 0 \text{ in \(B\) and \(u=0\) on \(\partial B\)}, \] satisfying \(\max u \in (b,c)\), where \(B\) is the unit ball in \(\mathbb{R}^n\) (\(n \geq 2\)), \(p > 2\), \(f\) is a continuously differentiable function such that \(f\) and \(f'\) satisfy appropriate sign conditions, and \(b, c\) are determined by \(f\). Using this fact, he shows that for \(a\) sufficiently large, the two solutions of this problem obtained by \textit{Z. Guo} and \textit{J. R. L. Webb} [J. Differ. Equ. 180, 1--50 (2002; Zbl 1014.35030)] are unique.
reviewed by: Marlène Frigon
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J40
zbMATH DE Number: 2173622
zbMATH Keywords: quasilinear elliptic Dirichlet problems
zbMATH Keywords: exact multiplicity
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
full work available at URL: j.na.2004.02.033
OpenAlex ID: W2007134308
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DOI: 10.1016/J.NA.2004.02.033
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description: scientific article; zbMATH DE number 2173622