On Semilinear Elliptic Equations with Hardy-Leray Potentials

Abstract

This paper is concerned with a semilinear elliptic equation with the Hardy-Leray potential. We employ the method of moving planes to prove the radial symmetry of positive solutions. Based on this result, we obtain the Liouville theorem in subcritical case. In addition, we find special radial solutions in critical case. All the properties above are similar to the corresponding results of the Lane-Emden equation.