Nonradial Solutions for the Henon Equation Close to the Threshold

Abstract

We consider the Henon problem {-Delta u = vertical bar x vertical bar(alpha)u(N+2+2 alpha/N-2-epsilon )in B-1, u > 0 in B-1, u = 0 on partial derivative B-1, where B-1 is the unit ball in R-N and N >= 3. For epsilon > 0 small enough, we use alpha as a parameter and prove the existence of a branch of nonradial solutions that bifurcates from the radial one when a is close to an even positive integer.