Nonautonomous (p,q)-equations with unbalanced growth and competing nonlinearities

We consider a parametric nonlinear Dirichlet problem driven by the double phase differential operator and a reaction that has the competing effects of parametric “concave” term and of a “convex” perturbation (concave-convex problem). Using variational tools together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least three nontrivial bounded solutions and we provide sign information for all of them (positive, negative and nodal). Moreover, the solutions are ordered.