An application of a mountain pass theorem
type: Item
instance of: scholarly article
title: An application of a mountain pass theorem
zbMATH Open document ID: 1018.35020
publication date: 2003-09-09T00:00:00Z
review text: The present paper is devoted to study the following Dirichlet problem: \[ -\Delta u=f(x,u), \quad x\in\Omega,\;u\in H^1_0(\Omega),\tag{1} \] where \(\Omega\) is a bounded smooth domain in \(\mathbb{R}^N\), with \(f(x,t)\) asymptotically linear in \(t\) at infinity. Under suitable assumption on \(f\), the author is using a version of the mountain pass theorem to prove existence of at least one positive solution of (1). The author indicates that his method also works for the case, when \(f(x,t)\) is superlinear in \(t\) at infinity.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1757443
zbMATH Keywords: asymptotically linear
zbMATH Keywords: superlinear
zbMATH Keywords: positive solution
author: Huansong Zhou
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s101140100147
OpenAlex ID: W2025942703
cites work: Dual variational methods in critical point theory and applications
cites work: Q3749777
cites work: Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
cites work: Variational elliptic problems which are nonquadratic at infinity
cites work: On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝN
cites work: Superlinear elliptic boundary value problems
cites work: A Variational Problem Related to Self-trapping of an Electromagnetic Field
cites work: Applying the mountain pass theorem to an asymptotically linear elliptic equation on RN
cites work: Nontrivial solutions for perturbations of the \(p\)-Laplacian on unbounded domains
cites work: Variational methods and semilinear elliptic equations
cites work: Q4692985
cites work: A Variation of the Mountain Pass Lemma and Applications
cites work: Q2715763
DOI: 10.1007/S101140100147
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1757443