A singular double phase eigenvalue problem with a superlinear indefinite perturbation

Abstract

We consider a Dirichlet problem driven by a double phase differential operator and a reaction which exhibits the combined effects of a parametric singular term and of an indefinite superlinear perturbation. The superlinearity condition on the perturbation is very general. Using variational tools, truncation and comparison techniques and critical groups, we prove an existence and multiplicity result which is global in the parameter (bifurcation-type result).