A perturbation result of semilinear elliptic equations in exterior strip domains

Tsing San Hsu; Hwai Chiuan Wang

doi:10.1017/S0308210500026858

A perturbation result of semilinear elliptic equations in exterior strip domains

Tsing San Hsu^*
, Hwai Chiuan Wang

^*Corresponding author for this work

National Tsing Hua University

Research output: Contribution to journal › Journal 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 = u^p + 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⊂R^m a bounded C^1,1 domain S = ω × Rⁿ, D is a bounded C^1,1 domain in R^m+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 language	English
Pages (from-to)	983-1004
Number of pages	22
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	127
Issue number	5
DOIs	https://doi.org/10.1017/S0308210500026858
State	Published - 1997
Externally published	Yes

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title = "A perturbation result of semilinear elliptic equations in exterior strip domains",

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, 1m 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\textbackslash{}D. In case f≡0, we assert that there is a positive higher-energy solution providing that D is small.",

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year = "1997",

doi = "10.1017/S0308210500026858",

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AU - Wang, Hwai Chiuan

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AB - 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, 1m 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.

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U2 - 10.1017/S0308210500026858

DO - 10.1017/S0308210500026858

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JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

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ER -

A perturbation result of semilinear elliptic equations in exterior strip domains

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