JournalsaihpcVol. 26, No. 5pp. 1701–1716

Existence and symmetry of least energy solutions for a class of quasi-linear elliptic equations

  • Louis Jeanjean

    Laboratoire de Mathématiques (UMR 6623), Université de Franche-Comté, 16, Route de Gray, 25030 Besançon Cedex, France
  • Marco Squassina

    Dipartimento di Informatica, Università degli Studi di Verona, Cá Vignal 2, Strada Le Grazie 15, 37134 Verona, Italy
Existence and symmetry of least energy solutions for a class of quasi-linear elliptic equations cover
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Abstract

For a general class of autonomous quasi-linear elliptic equations on Rn\mathbb{R}^{n} we prove the existence of a least energy solution and show that all least energy solutions do not change sign and are radially symmetric up to a translation in Rn\mathbb{R}^{n}.

Résumé

Pour une large classe d'équations quasilinéaires elliptiques autonomes sur RN\mathbb{R}^{N}, on montre l'existence d'une solution de moindre énergie. On montre aussi que toutes les solutions de moindres énergies ont un signe constant et sont, à une translation près, radiales.

Cite this article

Louis Jeanjean, Marco Squassina, Existence and symmetry of least energy solutions for a class of quasi-linear elliptic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 5, pp. 1701–1716

DOI 10.1016/J.ANIHPC.2008.11.003