Abstract: Motivated by important applications in nonlinear elasticity, recently
great attention has been devoted to the study of local and nonlocal nonlinear problems with (p, q) growth conditions.
We present existence results for a class of parametric (p, q) systems with
critical and Hardy terms in R^N, provided that the parameter is sufficiently large. The interest is twofold: on one hand, the simultaneous presence of critical terms, Hardy terms and the fact that the systems are studied in the whole R^N cause, roughly speaking,
a "triple loss of compactness" which dramatically affects the applicability of standard variational methods. On
the other hand, we compare the results obtained for the (p,q) fractional Laplacian operator with their local counterpart.
The results of the talk are obtained jointly with Patrizia Pucci.