Critical elliptic systems involving multiple strongly-coupled Hardy-type terms

In this paper, we study the radially-symmetric and strictly-decreasing solutions to a system of critical elliptic equations in R-N, which involves multiple critical nonlinearities and strongly-coupled Hardy-type terms. By the ODEs analysis methods, the asymptotic behaviors at the origin and infinity of solutions are proved. It is found that the singularities of u and v in the solution (u, v) are at the same level. Finally, an explicit form of least energy solutions is found under certain assumptions, which has all of the mentioned properties for the radial decreasing solutions.