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September/October 2009 Ground state solutions for a semilinear problem with critical exponent
Andrzej Szulkin, Tobias Weth, Michel Willem
Differential Integral Equations 22(9/10): 913-926 (September/October 2009).

Abstract

This work is devoted to the existence and qualitative properties of ground state solutions of the Dirchlet problem for the semilinear equation $-\Delta u-\lambda u=\vert u\vert^{2^*-2}u$ in a bounded domain. Here, $2^*$ is the critical Sobolev exponent, and the term ground state refers to minimizers of the corresponding energy within the set of nontrivial solutions. We focus on the indefinite case where $\lambda$ is larger than the first Dirichlet eigenvalue of the Laplacian, and we present a particularly simple approach to the study of ground states.

Citation

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Andrzej Szulkin. Tobias Weth. Michel Willem. "Ground state solutions for a semilinear problem with critical exponent." Differential Integral Equations 22 (9/10) 913 - 926, September/October 2009.

Information

Published: September/October 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35205
MathSciNet: MR2553063

Subjects:
Primary: 35J91
Secondary: 35B33, 35J20

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.22 • No. 9/10 • September/October 2009
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