Non degeneracy of the bubble in the critical case for non local equations

Abstract

We prove the nondegeneracy of the extremals of the fractional Sobolev inequality as solutions of a critical semilinear nonlocal equation involving the fractional Laplacian.

Cited by in corpus (5)

• Uniqueness and nondegeneracy of positive solutions of $\Ds u+u=u^p$ in ${\mathbb{R}}^N$ when $s$ is close to 1
• Solutions for a nonlocal elliptic equation involving critical growth and Hardy potential
• Linear non-degeneracy and uniqueness of the bubble solution for the critical fractional Hénon equation in ${\mathbb{R}}^N$
• Two-bubble nodal solutions for slightly subcritical Fractional Laplacian
• Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian