Weak solutions for a $(p(z),q(z))$-Laplacian Dirichlet problem

Abstract

We establish the existence of a nontrivial and nonnegative solution for a double phase Dirichlet problem driven by a $(p(z),q(z))$-Laplacian operator plus a potential term. Our approach is variational, but the reaction term $f$ need not satisfy the usual in such cases Ambrosetti-Rabinowitz condition.