Large solutions for the Laplacian with a power nonlinearity given by a variable exponent

  • José C. Sabina de Lis

    Dpto. de Análisis Matemático, Universidad de La Laguna, C/Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain
  • Jorge García-Melián

    Dpto. de Análisis Matemático, Universidad de La Laguna, C/Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain
  • Julio D. Rossi

    IMDEA Matematicas, C-IX, Campus Cantoblanco UAM, Madrid, Spain

Abstract

In this paper we consider positive boundary blow-up solutions to the problem in a smooth bounded domain . The exponent is allowed to be a variable positive Hölder continuous function. The issues of existence, asymptotic behavior near the boundary and uniqueness of positive solutions are considered. Furthermore, since is also allowed to take values less than one, it is shown that the blow up of solutions on is compatible with the occurrence of dead cores, i.e., nonempty interior regions where solutions vanish.

Cite this article

José C. Sabina de Lis, Jorge García-Melián, Julio D. Rossi, Large solutions for the Laplacian with a power nonlinearity given by a variable exponent. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 3, pp. 889–902

DOI 10.1016/J.ANIHPC.2008.03.007