Uniqueness and nondegeneracy of positive solutions of $\Ds u+u=u^p$ in $\R^N$ when $s$ is close to 1

Enrico Valdinoci; Mouhamed Moustapha Fall

arxiv: 1301.4868 · v2 · pith:DDBRSROTnew · submitted 2013-01-21 · 🧮 math.AP

Uniqueness and nondegeneracy of positive solutions of Ds u+u=u^p in R^N when s is close to 1

Mouhamed Moustapha Fall , Enrico Valdinoci This is my paper

classification 🧮 math.AP

keywords closeequationconsiderminimizernondegeneracynondegeneratepositivepossesses

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We consider the equation $\Ds u+u=u^p$, with $s\in(0,1)$ in the subcritical range of $p$. We prove that if $s$ is sufficiently close to 1 the equation possesses a unique minimizer, which is nondegenerate.

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Uniqueness and nondegeneracy of positive solutions of Ds u+u=u^p in R^N when s is close to 1

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