  We deal with a Dirichlet problem driven by the degenerate fractional
p-Laplacian and involving a nonlinear reaction which satisfies, among other
hypotheses, a (p-1)-linear growth at infinity with non-resonance above the
first eigenvalue. The energy functional governing the problem is thus
noncoercive. Thus we focus on the behavior of the reaction near the origin,
assuming that it has a (p-1)-sublinear growth at zero, vanishes at three
points, and satisfies a reverse Ambrosetti-Rabinowitz condition. Under such
assumptions, by means of critical point theory and Morse theory, and using
suitably truncated reactions, we show the existence of five nontrivial
solutions: two positive, two negative, and one nodal.
