Hénon equation with nolinearities involving Sobolev critical growth in H1 0,rad(B1)

Abstract

In this article we study the Hénon equation -Δu = λ|x|μu + |x|α|u|2*α-2u in B1, u = 0 on ∂B1, where B1 is the ball centered at the origin of RN (N ≥ 3) and μ ≥ α ≥ 0. Under appropriate hypotheses on the constant λ, we prove existence of at least one radial solution using variational methods.