Positive solutions of indefinite equations with p-Laplacian and supercritical nonlinearity

Abstract

This article is devoted to the study of the Dirichlet boundary problem for equations with p-Laplacian where n ≥ 1, 1 < p < q < +∞, and a(·) may change the sign in Ω. In the main result, we establish necessary and sufficient conditions when the problem possesses a weak positive solution with λ ∈ [λ1, λ*) where λ1 > 0 is the first eigenvalue of the Dirichlet p-Laplacian and λ* is an extremal point.