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Existence of two solutions of nonlinear elliptic equations with critical Sobolev exponents and mixed boundary conditions

Published online by Cambridge University Press:  14 November 2011

Feimin Huang
Feimin Huang
Affiliation:
Wuhan Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, P.R. China
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Abstract

Let Ω be a bounded domain in Rn(n ≧ 3) with Lipschitz-continuous boundary, ∂Ω = Γ0∪Γ1. In this paper we consider the following problem:

where φ ∈ L2 (Γ1), φ ≢ 0 on Γ1 and γ is the unit outward normal and p = 2n/(n − 2) = 2* is the critical exponent for the Sobolev embedding . We prove that for φ ∈ L2(Γ1) satisfying suitable conditions, the problem admits two solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 1 , 1996 , pp. 47 - 75
Copyright
Copyright © Royal Society of Edinburgh 1996

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