The Brezis--Nirenberg problem for the Hénon equation: ground state solutions

Abstract

This work is devoted to the Dirichlet problem for the equation (-Δu = λu + |x|^α|u|^{2^*-2} u) in the unit ball of $\mathbb{R}^N$. We assume that $λ$ is bigger than the first eigenvalues of the laplacian, and we prove that there exists a solution provided $α$ is small enough. This solution has a variational characterization as a ground state.

To appear on Advanced Nonlinear Studies