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

Abstract

AbstractWe prove existence results in all of $${\mathbb {R}}^N$$ R N for an elliptic problem of (p, q)-Laplacian type involving a critical term, nonnegative weights and a positive parameter $$\lambda $$ λ . In particular, under suitable conditions on the exponents of the nonlinearity, we prove existence of infinitely many weak solutions with negative energy when $$\lambda $$ λ 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.