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A perturbation result of semilinear elliptic equations in exterior strip domains

Published online by Cambridge University Press:  14 November 2011

Tsing-san Hsu  and
Hwai-chiuan Wang
Tsing-san Hsu
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan
Hwai-chiuan Wang
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan e-mail: [email protected]
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Synopsis

In this paper we show that if the decay of nonzero ƒ is fast enough, then the perturbation Dirichlet problem −Δu + u = up + ƒ(z) in Ω has at least two positive solutions, where

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 ƒ ≡ 0, we assert that there is a positive higher-energy solution providing that D is small.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 5 , 1997 , pp. 983 - 1004
Copyright
Copyright © Royal Society of Edinburgh 1997

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