An improved bound for the non-existence of radial solutions of the Brezis-Nirenberg problem in Hn

TL;DR

This paper improves the bounds on the eigenvalues that determine the non-existence of radial solutions for a specific nonlinear PDE on geodesic balls in hyperbolic space, using advanced analytical techniques.

Contribution

It provides a sharper eigenvalue bound for the Brezis-Nirenberg problem in hyperbolic space, extending previous non-existence results.

Findings

Derived an improved eigenvalue bound for non-existence of solutions

Applied Rellich-Pohozaev and Hardy's inequalities in hyperbolic geometry

Extended non-existence results to a broader parameter range

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 Hn, for 2<n<4.