Positive stationary solutions for p-Laplacian problems with nonpositive perturbation

The paper is devoted to the existence of positive solutions of non-linear elliptic equations with p-Laplacian. We provide a general topological degree that detects solutions of the problem {A(u)= F(u), u is an element of M where A : X superset of D(A) -> X* is a maximal monotone operator in a Banach space X and F: M -> X* is a continuous mapping defined on a closed convex cone M subset of X. Next, we apply this general framework to a class of partial differential equations with p-Laplacian under Dirichlet boundary conditions. In the paper we employ general ideas from Cwiszewski and Kryszewski (2009) [5], where a setting suitable for the one dimensional p-Laplacian was introduced. (C) 2012 Elsevier Inc. All rights reserved.