A perturbation result of semilinear elliptic equations in exterior strip domains

Tsing San Hsu*, Hwai Chiuan Wang

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

14 Scopus citations

Abstract

In this paper we show that if the decay of nonzero f is fast enough, then the perturbation Dirichlet problem -Δu + u = up + f(z) in Ω has at least two positive solutions, where N = m+n, m≧3, n≧1, 1<p< N+2/N-2, ω⊂Rm a bounded C1,1 domain S = ω × Rn, D is a bounded C1,1 domain in Rm+n such that D⊂⊂S and Ω=S\D. In case f≡0, we assert that there is a positive higher-energy solution providing that D is small.

Original languageEnglish
Pages (from-to)983-1004
Number of pages22
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume127
Issue number5
DOIs
StatePublished - 1997
Externally publishedYes

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