Multiple finite energy solutions of critical semilinear field equations
type: Item
instance of: scholarly article
title: Multiple finite energy solutions of critical semilinear field equations
zbMATH Open document ID: 0865.35045
author: E. S. Noussair
author: Charles A. Swanson
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-07-10T00:00:00Z
review text: The authors obtain, by using minimax methods and exploring compactness arguments, existence and multiplicity results of solutions of the semilinear elliptic problem \[ -\Delta u=p_0|u|^{\tau-1}u+q(x)|u|^{\gamma-1}u\quad\text{in }\mathbb{R}^N,\quad u\not\equiv 0,\quad u\in D^{1,2}_0(\mathbb{R}^N),\tag{1} \] where \(N\geq 3\), \(\tau+1=2N/(N-2)\), \(1<\gamma<\tau\), \(p_0\) is a positive constant, and \(q\) is a nonnegative \(L^\infty_{\text{loc}}\) function. Qualitative properties such as the signs of the solutions of (1) and their asymptotic behaviour are studied.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 861763
zbMATH Keywords: multiplicity
zbMATH Keywords: signs of the solutions
reviewed by: José Valdo A. Gonçalves
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1355
OpenAlex ID: W2059065288
DOI: 10.1006/JMAA.1995.1355
description: scientific article; zbMATH DE number 861763