Semilinear elliptic equations with sublinear indefinite nonlinearities
type: Item
instance of: scholarly article
title: Semilinear elliptic equations with sublinear indefinite nonlinearities
zbMATH Open document ID: 0952.35052
author: Stan Alama
published in: Advances in Differential Equations
publication date: 2000-08-21T00:00:00Z
review text: It is considered the Neumann problem for \[ -\Delta u - \lambda u = a(x)u^q + \gamma u^p, \quad u\geq 0, \] in a bounded, smooth domain \(\Omega\subset\mathbb{R}^N\). Here are \(0<q<1<p\), \(\lambda\in\mathbb{R}\), \(\gamma\geq 0\), and \(a\in C^{\beta}\), \(\beta\in (0,1]\). The novelty in the problem is some combined effect of \(\text{sign} a(x)\) indefiniteness and the non-Lipschitz character of \(u^q\) near zero. That sort of problems includes some population ecology equations.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 58E07
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 1493616
zbMATH Keywords: nonlinear elliptic Neumann problem
zbMATH Keywords: sublinear indefinite nonlinearity
zbMATH Keywords: bifurcation analysis
zbMATH Keywords: variational methods
zbMATH Keywords: sub-solutions
zbMATH Keywords: super-solutions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1493616