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arXiv · 1201.3736

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

Simone Secchi
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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.

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Simone Secchi. 2012-01-18. The Brezis--Nirenberg problem for the Hénon equation: ground state solutions. https://arxiv.org/abs/1201.3736

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