Ground state and multiple solutions for a critical exponent problem

We study the following Brezis–Nirenberg type critical exponent equation which is related to the Yamabe problem: where Ω is a smooth bounded domain in and 2 * is the critical Sobolev exponent. We show that, if N ≥ 5, this problem has at least pairs of nontrivial solutions for each fixed λ ≥ λ 1 , whe...

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Bibliographic Details
Published in:Nonlinear differential equations and applications 2012-06, Vol.19 (3), p.253-277
Main Authors: Chen, Z., Shioji, N., Zou, W.
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:We study the following Brezis–Nirenberg type critical exponent equation which is related to the Yamabe problem: where Ω is a smooth bounded domain in and 2 * is the critical Sobolev exponent. We show that, if N ≥ 5, this problem has at least pairs of nontrivial solutions for each fixed λ ≥ λ 1 , where λ 1 is the first eigenvalue of −Δ with the Dirichlet boundary condition. For N ≥ 3, we give energy estimates from below for ground state solutions.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-011-0127-0