Liouville results for -Laplace equations of Lane–Emden–Fowler type

  • Berardino Sciunzi

    Università della Calabria, Dipartimento di Matematica, V.P. Bucci, Arcavacata di Rende (CS), Italy
  • Lucio Damascelli

    Università di Roma Tor Vergata, Dipartimento di Matematica, Via della ricerca scientifica, 1, I-00133 Rome, Italy
  • Alberto Farina

    LAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, Faculté de Mathématiques et d'Informatique, 33, rue Saint-Leu, 80039 Amiens Cedex 1, France
  • Enrico Valdinoci

    Università di Roma Tor Vergata, Dipartimento di Matematica, Via della ricerca scientifica, 1, I-00133 Rome, Italy

Abstract

We consider sign changing solutions of the equation in possibly unbounded domains or in . We prove Liouville type theorems for stable solutions or for solutions which are stable outside a compact set. The results hold true for and . Here is a new critical exponent, which is infinity in low dimension and is always larger than the classical critical one.

Cite this article

Berardino Sciunzi, Lucio Damascelli, Alberto Farina, Enrico Valdinoci, Liouville results for -Laplace equations of Lane–Emden–Fowler type. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 4, pp. 1099–1119

DOI 10.1016/J.ANIHPC.2008.06.001