A critical surface for the solutions to singular elliptic systems

Abstract

In this paper, we mainly study the radially-symmetric and strictly-decreasing solutions to a system of critical elliptic equations in R N , which involves strongly-coupled critical nonlinearities and different Hardy-type terms. By the ODEs analysis methods, the asymptotic behaviors at the origin and infinity of solutions are proved. By the way, the asymptotic properties of radial and decreasing minimizers to the related best Sobolev constant are established. We find the existence of a critical surface, above which and below which the asymptotic properties of solutions are deferent.