On existence of solution for a class of semilinear elliptic equations with nonlinearities that lies between different powers
type: Item
instance of: scholarly article
title: On existence of solution for a class of semilinear elliptic equations with nonlinearities that lies between different powers
zbMATH Open document ID: 1187.35064
DOI: 10.1155/2008/578417
author: Marco A. Souto
author: Claudianor O. Alves
published in: Abstract and Applied Analysis
publication date: 2008-08-19T00:00:00Z
full work available at URL: https://eudml.org/doc/45272
review text: Summary: We prove that the semilinear elliptic equation \( - \Delta u=f(u)\) in \(\Omega\), \(u=0\) on \(\partial\Omega\) has a positive solution when the nonlinearity \(f\) belongs to a class which satisfies \(\mu t^q\leq f(t)\leq Ct^p\) at infinity and behaves like \(t^q\) near the origin, where \(1<q<(N+2)/(N-2)\) if \(N\geq 3\) and \(1<q<+\infty\) if \(N=1,2\). In our approach, we do not need the Ambrosetti-Rabinowitz condition, and the nonlinearity does not satisfy any hypotheses required by the blowup method. Furthermore, we do not impose any restriction on the growth of \(p\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 5313191
zbMATH Keywords: semilinear elliptic equation
zbMATH Keywords: positive solution
Wikidata QID: Q58644364
MaRDI profile type: Publication
OpenAlex ID: W2068535948
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description: scientific article; zbMATH DE number 5313191