Positive solutions for parametric equidiffusive p-Laplacian equations

We consider a parametric Dirichlet problem driven by the p-Laplacian with a Carathéodory reaction of equidiffusive type. Our hypotheses incorporate as a special case the equidiffusive p-logistic equation. We show that if is the principal eigenvalue of the Dirichlet negative p-Laplacian and (λ being the parameter), the problem has a unique positive solution, while for , the problem has no positive solution.