On the solvability of a semilinear elliptic equation via an associated eigenvalue problem
type: Item
instance of: scholarly article
title: On the solvability of a semilinear elliptic equation via an associated eigenvalue problem
zbMATH Open document ID: 0853.35039
DOI: 10.1007/PL00004520
published in: Mathematische Zeitschrift
publication date: 1996-09-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174861
review text: We study a boundary value problem for the equation \(- \Delta u= \lambda u- h(x) f(u)\), where \(f\) grows superlinearly and \(h(x)\geq 0\) may vanish on a set with a nonempty interior. We observe that the existence, nonexistence, and multiplicity of solutions is determined by the solvability of an associated linear eigenvalue problem. In particular, under certain assumptions we show that the nonlinear problem possesses a nontrivial solution if and only if the associated eigenvalue problem is solvable.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35P20
zbMATH DE Number: 922489
zbMATH Keywords: semilinear elliptic equation
zbMATH Keywords: existence
zbMATH Keywords: nonexistence
zbMATH Keywords: multiplicity of solutions
author: Stan Alama
author: G. Tarantello
MaRDI profile type: Publication
Wikidata QID: Q60143359
OpenAlex ID: W1993780107
description: scientific article; zbMATH DE number 922489