Periodic solutions for parabolic fractional p-Laplacian problems via topological degree

In this work, we consider the nonlinear parabolic initial boundary value problem involving the fractional p-Laplacian operator. We employ topological degree methods to establish the existence of a time periodic nontrivial weak solutions in the appropriate space X := L-p(0,T ; W (s,p )(O)). Our approach to proving the main result is based on transforming this nonlinear parabolic problem into an operator equation of the shape Ku+Bu=h , where B is of type (S+) relative in the domain of densely defined linear maximal monotone operator K.