A resonance problem for non-local elliptic operators

In this paper we consider a resonance problem driven by a non-local integrodifferential operator L-K with homogeneous Dirichlet boundary conditions. This problem has a variational structure and we find a solution for it using the Saddle Point Theorem. We prove this result for a general integrodifferential operator of fractional type and from this, as a particular case, we derive an existence theorem for a fractional Laplacian equation. This existence theorem extends to the non-local setting some results, already known in the literature in the case of the Laplace operator