Positive stationary solutions for p-Laplacian problems with nonpositive perturbation

The paper is devoted to the existence of positive solutions of nonlinear elliptic equations with p-Laplacian. We provide a general topological degree that detects solutions of the problem{A(u)=F(u),u∈M where A:X⊃D(A)→X⁎A:X⊃D(A)→X⁎ is a maximal monotone operator in a Banach space X   and F:M→X⁎F:M→X⁎ is a continuous mapping defined on a closed convex cone M⊂XM⊂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 Ćwiszewski and Kryszewski (2009) [5], where a setting suitable for the one dimensional p-Laplacian was introduced.