On Symmetric Solutions for (p, q)-Laplacian Equations in R^N with Critical Terms

We prove existence and multiplicity results in RN for an elliptic problem of (p,q)-Laplacian type with a nonlinearity involving both a critical term and a subcritical term with a positive real parameter λ. In particular, nonnegative nontrivial weights satisfying some symmetry conditions with respect to a certain group T are included in the nonlinearity. We prove first the existence of at least one solution with positive energy for λ sufficiently small using Mountain Pass Theorem, then we obtain the existence of infinitely many weak solutions with positive (finite) energy for every λ positive applying Fountain Theorem. Our proofs use variational methods and the concentration compactness principles.