# A Non-Existence Result for a Generalized Radial Brezis-Nirenberg Problem

## TL;DR

This paper introduces a novel method combining Rellich--Pohozaev and Hardy inequalities to determine spectral parameter regions where the generalized Brezis--Nirenberg problem admits no non-trivial smooth solutions, especially improving estimates in low dimensions.

## Contribution

It presents a new approach that enhances spectral estimates for the generalized Brezis--Nirenberg problem by integrating classical inequalities.

## Key findings

- Derived improved spectral bounds for low-dimensional cases.
- Established a new method combining Rellich--Pohozaev and Hardy inequalities.
- Identified regions with no non-trivial solutions for the problem.

## Abstract

We develop a new method for estimating the region of the spectral parameter of a generalized Brezis--Nirenberg problem for which there are no, non trivial, smooth solutions. This new method combines the standard Rellich--Pohozaev argument with a Hardy type inequality for bounded domains. The estimates we get are better than the usual estimates for low dimensions.