摘要 : In this paper, we consider nonlinear equations involving the fractional p-Laplacian(?△)psu(x))≡Cn,spPV∫Rn|u(x)?u(y)|p?2[u(x)?u(y)]|x?y|n+spdy=f(x,u).We prove amaximum principle for anti-symmetric functionsand obtain other key ing... 展开 In this paper, we consider nonlinear equations involving the fractional p-Laplacian(?△)psu(x))≡Cn,spPV∫Rn|u(x)?u(y)|p?2[u(x)?u(y)]|x?y|n+spdy=f(x,u).We prove amaximum principle for anti-symmetric functionsand obtain other key ingredients for carrying on the method of moving planes, such as a variant of the Hopf Lemma –a boundary estimate lemmawhich plays the role of thenarrow region principle. Then we establish radial symmetry and monotonicity for positive solutions to semilinear equations involving the fractional p-Laplacian in a unit ball and in the whole space. We believe that the methods developed here can be applied to a variety of problems involving nonlinear nonlocal operators. 收起