On positive entire solutions to a class of equations with a singular coefficient and critical exponent

Abstract

We prove some results about existence, uniqueness and qualitative behavior of positive solutions to equations of the type depending on the behavior of the function a of the angular variable x/|x|. Our main results concern the critical nonlinearity f(s) = s(n+2)/(n-2) The proofs are based on variational arguments and the moving plane method.