  We study a Dirichlet-type boundary value problem for a pseudo-differential
equation driven by the fractional Laplacian, with a non-linear reaction term
which is resonant at infinity between two non-principal eigenvalues: for such
equation we prove existence of a non-trivial solution. Under further
assumptions on the behavior of the reaction at zero, we detect at least three
non-trivial solutions (one positive, one negative, and one of undetermined
sign). All results are based on the properties of weighted fractional
eigenvalues, and on Morse theory.
