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Existence of multiple positive solutions for a semilinear equation with critical exponent*

Published online by Cambridge University Press:  14 November 2011

Deng Yinbing
Deng Yinbing
Affiliation:
Department of Mathematics, Huazhong Normal University, Wuhan 430070, P.R. China
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Synopsis

In this paper we discuss the problem

We show that for c > 0 there exists a positive constant μ* such that (*)μ possesses at least one solution if μ ∈ (0, μ*) and no solutions if μ > μ*. Furthermore, there exists a positive constant μ**≦μ* such that (*)μ possesses at least two solutions if μ∈(0, μ**), 2<N<6. For N≧6, μ∈(0,μ**), we show that problem (*)μ possesses a unique solution if f(x) is radial with f′(r) < 0(r = |x|).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 122 , Issue 1-2 , 1992 , pp. 161 - 175
Copyright
Copyright © Royal Society of Edinburgh 1992

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