We investigate problems connected to the stability of the well-known Pohožaev obstruction. We generalize results which were obtained in the minimizing setting by Brezis and Nirenberg  and more recently in the radial situation by Brezis and Willem .
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Olivier Druet, Paul Laurain, Stability of the Pohožaev obstrucion in dimension 3. J. Eur. Math. Soc. 12 (2010), no. 5, pp. 1117–1149DOI 10.4171/JEMS/225