On a class of superlinear (p,q)-Laplacian type equations on R^N

Starting from a new sum decomposition of $ W^{1,p}(R^N)cap W^{1,q}(R^N)$ and using a variational approach, we investigate the existence of multiple weak solutions of a (p,q)-Laplacian equation on $R^N$, for 1 < q < p < N, with a sign-changing potential and a Caratheodory reaction term satisfying the celebrated Ambrosetti-Rabinowitz condition. Our assumptions are mild and different from those used in related papers and moreover our results improve or complement previous ones for the single p-Laplacian