Multiplicity results for (p,q)-Laplacian equations with critical exponent in R^N and negative energy

We prove existence results in all of R^N for an elliptic problem of (p,q)-Laplacian type involving a critical term, nonnegative weights and a positive parameter lambda. In particular, under suitable conditions on the exponents of the nonlinearity, we prove existence of infinitely many weak solutions with negative energy when lambda belongs to a certain interval. Our proofs use variational methods and the concentration compactness principle. Towards this aim we give a detailed proof of tight convergence of a suitable sequence.