Radial symmetry and monotonicity for an integral equation

In this paper we study radial symmetry and monotonicity of positive solutions of an integral equation arising from some higherorder semilinear elliptic equations in the whole space Rn. Instead of the usual method of moving planes, we use a new Hardy– Littlewood–Sobolev (HLS) type inequality for the Bessel potentials to establish the radial symmetry and monotonicity results. © 2007 Elsevier Inc. All rights reserved.