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

This article is devoted to the study of the Dirichlet boundary problem for equations with p-Laplacian -Delta(p)u - lambda vertical bar u vertical bar(p-2)u = a(x)vertical bar u vertical bar(q-2)u, in Omega subset of R-n, where n >= 1, 1 < p < q < +infinity, and a(.) may change the sign in Omega. In the main result, we establish necessary and sufficient conditions when the problem possesses a weak positive solution with lambda is an element of[lambda(1), lambda*) where lambda(1) > 0 is the first eigenvalue of the Dirichlet p-Laplacian and lambda* is an extremal point.