Nonradial solutions for the H\'enon equation in $R^N$

Abstract

In this paper we consider the problem $$ {ll} -\Delta u=(N+\a)(N-2)|x|^{\a}u^\frac{N+2+2\a}{N-2} & in R^N u>0& in R^N u\in D^{1,2}(R^N). $$ where $N\ge3$. From the characterization of the solutions of the linearized operator, we deduce the existence of nonradial solutions which bifurcate from the radial one when $\alpha$ is an even integer.