Stability of the Poho\v{z}aev obstrucion in dimension 3

TL;DR

This paper studies the stability of the Pohožaev obstruction in three dimensions, extending previous results from minimizing and radial cases to a broader context.

Contribution

It generalizes existing stability results of the Pohožaev obstruction beyond minimizing and radial settings to more general scenarios in three dimensions.

Findings

Extended stability results of the Pohožaev obstruction to new settings

Generalized previous work by Brezis and Nirenberg, Brezis and Willem

Provided insights into the behavior of solutions related to the Pohožaev obstruction

Abstract

We investigate problems connected to the stability of the wellknown Poho\v{z}aev obstruction. We generalize results which were obtained in the minimizing setting by Brezis and Nirenberg [2] and more recently in the radial situation by Brezis and Willem [3].