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2005 Multiple solutions for the Brezis-Nirenberg problem
Mónica Clapp, Tobias Weth
Adv. Differential Equations 10(4): 463-480 (2005).

Abstract

We establish the existence of multiple solutions to the Dirichlet problem for the equation \[ -\Delta u=\lambda u+|u|^{\frac{4}{N-2}}u \] on a bounded domain $\Omega$ of $\mathbb{R}^{N},$ $N\geq4.$ We show that, if $\lambda>0$ is not a Dirichlet eigenvalue of $-\Delta$ on $\Omega,$ this problem has at least $\frac{N+1}{2}$ pairs of nontrivial solutions. If $\lambda$ is an eigenvalue of multiplicity $m$ then it has at least $\frac{N+1-m}{2}$ pairs of nontrivial solutions.

Citation

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Mónica Clapp. Tobias Weth. "Multiple solutions for the Brezis-Nirenberg problem." Adv. Differential Equations 10 (4) 463 - 480, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1284.35151
MathSciNet: MR2122698

Subjects:
Primary: 35J20
Secondary: 35J60, 47J30

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.10 • No. 4 • 2005
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