Ground state and nodal solutions for a class of double phase problems

We consider a double phase problem driven by the sum of the p-Laplace operator and a weighted q-Laplacian (q < p), with a weight function which is not bounded away from zero. The reaction term is (p - 1)-superlinear. Employing the Nehari method, we show that the equation has a ground state solution of constant sign and a nodal (sign-changing) solution.