Solvability for a fractional $ p $-Laplacian equation in a bounded domain

Abstract

<abstract><p>In this paper we use the topological degree and the fountain theorem to study the existence of weak solutions for a fractional $ p $-Laplacian equation in a bounded domain. For the nonlinearity $ f $, we consider two situations: (1) the non-resonance case where $ f $ is $ (p-1) $-asymptotically linear at infinity; (2) the resonance case where $ f $ satisfies the Landesman-Lazer type condition.</p></abstract>