A Liouville's theorem for a fractional elliptic system with indefinite nonlinearities

Abstract

In this paper, we consider a fractional elliptic system with indefinite nonlinearities. We prove that every positive bounded solution of the system is monotone increasing along x1 direction by using the direct method of moving planes. Based on this monotonicity, we obtain the nonexistence of positive solutions and a Liouville type results for the fractional elliptic system. As an application, we get the Liouville type results for the fractional elliptic system with cubic nonlinearities.