JournalsaihpcVol. 25, No. 1pp. 173–179

Finite Morse index solutions of exponential problems

  • E.N. Dancer

    School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia
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Abstract

We prove that the problem Δu=eu−\mathrm{\Delta }u = \mathrm{e}^{u} has no negative finite Morse index solution on R3\mathbb{R}^{3} and give some applications to bounded domain problems.

Résumé

Nous montrons que le problème Δu=eu−\mathrm{\Delta }u = \mathrm{e}^{u} ne possède pas de solution négative d'indice de Morse fini sur R3\mathbb{R}^{3} et présentons quelques applications à des problèmes sur des domaines bornés.

Cite this article

E.N. Dancer, Finite Morse index solutions of exponential problems. Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 1, pp. 173–179

DOI 10.1016/J.ANIHPC.2006.12.001