Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball

摘要

In this paper, we study a nonlinear system involving the fractional p-Laplacian in a unit ball and establish the radial symmetry and monotonicity of its positive solutions. By using the direct method of moving planes, we prove the following result. For , if and satisfy the following nonlinear system and are nonnegative continuous functions satisfying the following (i) and are increasing for ; (ii) , are bounded near . Then the positive solutions must be radially symmetric and monotone decreasing about the origin.