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

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.