Singular Anisotropic Problems with Competition Phenomena

Abstract

We consider a Dirichlet problem driven by the anisotropic (p(z), q(z))-Laplacian, with a parametric reaction exhibiting the combined effects of singular and concave-convex nonlinearities. The superlinear term may change sign. Using variational tools together with truncation and comparison techniques, we prove a global (for the parameter ? > 0) existence and multiplicity theorem (a bifurcation-type theorem).