Positive solutions of a class of nonlinear eigenvalue problems
type: Item
instance of: scholarly article
title: Positive solutions of a class of nonlinear eigenvalue problems
zbMATH Open document ID: 1050.35060
author: Zhaoli Liu
published in: Mathematische Zeitschrift
publication date: 2004-06-17T00:00:00Z
review text: The author studies positive solutions of \[ \begin{aligned} \Delta u + \lambda f(u) & = 0\quad\text{in }\Omega,\\ u&= 0\quad\text{in }\partial\Omega.\end{aligned} \] Here \(f(0) > 0\) and \(f\) has \(n\) different zeros for positive values \(a_k\), \(\lambda\) is a positive parameter. An important geometrical assumption in this work is that \(\Omega\) is symmetric and convex in \(N\) orthogonal directions. The author then proves a number of results, mainly concerning the number of solutions as well as bounds for the solutions. An example would be \(f(u) = d + \cos u\), \(0 < d < 1\).
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 2075748
zbMATH Keywords: symmetric convex domain
zbMATH Keywords: number and bounds of solutions
reviewed by: René Sperb
MaRDI profile type: Publication
full work available at URL: s002090100373
OpenAlex ID: W1966568938
DOI: 10.1007/S002090100373
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description: scientific article; zbMATH DE number 2075748