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Existence of two solutions of nonlinear elliptic equations with critical Sobolev exponents and mixed boundary conditions
- Source :
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 126:47-75
- Publication Year :
- 1996
- Publisher :
- Cambridge University Press (CUP), 1996.
-
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.
Details
- ISSN :
- 14737124 and 03082105
- Volume :
- 126
- Database :
- OpenAIRE
- Journal :
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Accession number :
- edsair.doi...........5268432e577f2ad7e35779b3512e29b8