Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems

Abstract

We consider an eigenvalue problem driven by the anisotropic (p, q)-Laplacian and with a Carathéodory reaction which is (p(z) − 1)-sublinear as x → + ∞. We look for positive solutions. We prove an existence, nonexistence and multiplicity theorem which is global in the parameter λ > 0, that is, we prove a bifurcation-type theorem which describes in an exact way the changes in the set of positive solutions as the parameter λ varies on ℝ̊+ = (0, + ∞).