Positive Solutions for Resonant (p,q)-equations with convection

We consider a nonlinear parametric Dirichlet problem driven by the (p,q)-Laplacian (double phase problem) with a reaction exhibiting the competing effects of three different terms. Aparametric one consisting of the sum of a singular term and of a drift term (convection) and of a nonparametric perturbation which is resonant. Using the frozen variable method and eventually a fixed point argument based on an iterative asymptotic process, we show that the problem has a positive smooth solution.