2014, Fiscella, Alessio, Servadei, Raffaella, Valdinoci, Enrico

In this paper we study a non-local fractional Laplace equation, depending on a parameter, with asymptotically linear right-hand side. Our main result concerns the existence of weak solutions for this equation and it is obtained using variational and topological methods. We treat both the nonresonant case and the resonant one.

2013, Fiscella, Alessio, Valdinoci, Enrico

We show the existence of non-negative solutions for a Kirchhoff type problem driven by a non-local integrodifferential operator.

2013, Albanese, Guglielmo, Fiscella, Alessio, Valdinoci, Enrico

We prove a regularity theory in the Gevrey class for a family of nonlocal differential equations of elliptic type.