A fixed point method for the p(.)-Laplacian

A topological method, based on the fundamental properties of the Leray-Schauder degree, is used in proving the existence of a week solution in W(0)(1,p(.)) (Omega) to Dinchlet problem -div(vertical bar del u vertical bar(p(x)-2)del u) = f(x , u), x epsilon Omega, (P) u = 0, x epsilon partial derivative Omega. This method is an adaptation of that used by Dinca et al. [G. Dinca, P. Jebelean, Une methode de point fixe pour le p-laplacien, C. R. Acad. Sci. Paris, Ser. I 324 (1997) 165-168. [1], G. Dinca, P. Jebelean. J. Mawhin, Variational and topological methods for Dirichlet problems with p-Laplacian, Portugal. Math. 53 (3) (2001) 339-377. [2]] for Dirichlet problems with classical p-Laplacian (p(x) equivalent to p = const. > 1). To cite this article: G. Dinca, C R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.