Multiplicity of positive solutions for semilinear elliptic systems

Tsing San Hsu*

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

1 Scopus citations

Abstract

We study the effect of the coefficient h(x) of the critical nonlinearity on the number of positive solutions for semilinear elliptic systems. Under suitable assumptions for f(x), g(x), and h(x), we should prove that for sufficiently small ,>0, there are at least k+1 positive solutions of the semilinear elliptic systems -Δu=f(x)|u|q-2u+(α/ (α+β))h(x)|u|α-2u|v|β, -Δv=g(x)|v|q-2v+(β/(α+β))h(x)|u| α|v|β-2v, where 0εΩ⊂R N is a bounded domain, α>1, β>1, and N/(N-2)<q<2<α+β=2* for N>4.

Original languageEnglish
Article number746380
JournalAbstract and Applied Analysis
Volume2013
DOIs
StatePublished - 2013

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