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Ground state solutions for a semilinear problem with critical exponent
Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
Institut für Mathematik, Goethe-Universität Frankfurt, Germany.
Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.
2009 (English)In: Differential and Integral Equations, ISSN 0893-4983, Vol. 22, no 9-10, 15 p.913-926 p.Article in journal (Refereed) Published
##### Abstract [en]

This work is devoted to the existence and to 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.

##### Place, publisher, year, edition, pages
Athens, Ohio: Khayyam Publishing Company , 2009. Vol. 22, no 9-10, 15 p.913-926 p.
##### Keyword [en]
Semilinear Dirichlet problem, critical exponent, ground state, Morse index, radial solutions
##### National Category
Mathematical Analysis
Mathematics
##### Identifiers
ISI: 000277456500009OAI: oai:DiVA.org:su-16778DiVA: diva2:183298
Available from: 2008-12-23 Created: 2008-12-23 Last updated: 2010-01-04Bibliographically approved

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Szulkin, Andrzej
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Differential and Integral Equations
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Mathematical Analysis