Liouville-type theorems for a system of fractional Laplacian equations

Abstract

In the paper, we study the following system of partial differential equations (PDEs) involving fractional Laplacian operators (1) under the boundary conditions , where , , and . In order to overcome the difficulty that there are no corresponding maximum principles for the operators and in , we employ the method of moving planes in integral forms to the system of integral equations which is equivalent to System (1). Then, we obtain some Liouville type theorems for a pair of solutions of System (1) under different assumptions.