non-dengeneracy of solutions for prescribled scalar curvature problem via local Pohozaev identity
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Abstract
This paper deals with the following nonlinear elliptic equation $$-\Delta u=Q(|y'|,y'')u^{\frac{N+2}{N-2}},\,\,u>0,\,\,\text{in}\R^N,\,\,u\inD^{1,2}(\R^{N}),$$where $(y',y'')\in \R^2\times\R^{N-2}$, where $Q(|y'|,y'')$ is a bounded non-negative function in $\mathbb{R}^{2}\times \R^{N-2}$. We prove a non-degeneracy result for the positive solutions constructed in [PWW].
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- last seen: 2026-05-19T01:45:01.086888+00:00