Radial symmetry for a generalized nonlinear fractional p-Laplacian problem

Abstract

This paper first introduces a generalized fractional p-Laplacian operator (–Δ)sF;p. By using the direct method of moving planes, with the help of two lemmas, namely decay at infinity and narrow region principle involving the generalized fractional p-Laplacian, we study the monotonicity and radial symmetry of positive solutions of a generalized fractional p-Laplacian equation with negative power. In addition, a similar conclusion is also given for a generalized Hénon-type nonlinear fractional p-Laplacian equation.

Keywords

• generalized fractional p-Laplacian
• method of moving planes
• negative powers
• radial symmetry and monotonicity