  We consider a Dirichlet type problem for a nonlinear, nonlocal equation
driven by the degenerate fractional p-Laplacian, whose reaction combines a
sublinear term depending on a positive parameter and an asymmetric perturbation
(superlinear at positive infinity, at most linear at negative infinity). By
means of critical point theory and Morse theory, we prove that, for small
enough values of the parameter, such problem admits at least four nontrivial
solutions: two positive, one negative, and one nodal. As a tool, we prove a
Brezis-Oswald type comparison result.
