  We study a nonlinear elliptic equation driven by the degenerate fractional
p-Laplacian, with Dirichlet type condition and a jumping reaction, i.e.,
(p-1)-linear both at infinity and at zero but with different slopes crossing
the principal eigenvalue. Under two different sets of hypotheses, entailing
different types of asymmetry, we prove the existence of at least two nontrivial
solutions. Our method is based on degree theory for monotone operators and
nonlinear fractional spectral theory.
