Existence results for fractional p-Laplacian problems via Morse theory

We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-linear\r\nproblems involving the fractional Laplacian and arising in the framework of continuum mechanics, phase\r\ntransition phenomena, population dynamics and game theory. Under dierent growth assumptions on the\r\nreaction term, we obtain various existence as well as finite multiplicity results by means of variational and\r\ntopological methods and, in particular, arguments from Morse theory.