WIAS Preprint No. 1804, (2013)

Uniqueness and nondegeneracy of positive solutions of $(-Delta)^s u+u = u^p$ in $R^N$ when $s$ is close to 1


  • Fall, Mouhamed Moustapha
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 26A33 35A15 35B40


  • Fractional Laplacian, uniqueness results, nondegeneracy of minimizers, asymptotic methods


We consider the equation (-Δ)s u+u = up with s ∈ (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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