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

We prove some results about existence, uniqueness and qualitative behavior of positive solutions to equations of the type -Δ u=a(x/|x|)u |x|²+f(x,u)\;\;in \;Rⁿ\0\\;, 0.1 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.