Four Solutions for Fractional p-Laplacian Equations with Asymmetric Reactions

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