Parabolic logistic equation with harvesting involving the fractional Laplacian

Abstract

This paper deals with a class of parabolic reaction-diffusion equations driven by the fractional Laplacian as the diffusion operator over a bounded domain with zero Dirichlet external condition. Using a comparison principle and monotone iteration method, we establish existence and uniqueness results. We apply the existence result to the logistic growth problems with constant yield harvesting by constructing an ordered pair of positive sub- and supersolution of the corresponding elliptic problem.