An improved bound for the non-existence of radial solutions of the Brezis–Nirenberg problem in $\mathbb H^n$

Rafael D. Benguria; Soledad Benguria

doi:10.4171/175

BooksecrCollected Volumepp. 153–160

An improved bound for the non-existence of radial solutions of the Brezis–Nirenberg problem in $H^{n}$

Rafael D. Benguria
Pontificia Universidad Católica de Chile, Santiago de Chile, Chile
Soledad Benguria
University of Wisconsin, Madison, USA

$An improved bound for the non-existence of radial solutions of the Brezis–Nirenberg problem in $\mathbb H^n$ cover$

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Abstract

Using a Rellich–Pohozaev argument and Hardy's inequality, we derive an improved bound on the nonlinear eigenvalue for the non existence of radial solutions of a Brezis–Nirenberg problem, with Dirichlet boundary conditions, on a geodesic ball of $H^{n}$ , for $2 < n < 4$ .