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

Abstract

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.

References in corpus (2)

• Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian
• Non degeneracy of the bubble in the critical case for non local equations

Cited by in corpus (2)

• Multiple Semiclassical Standing Waves for Fractional Nonlinear Schrödinger Equations
• Existence and multiplicity of solutions for a nonlinear Schrödinger equation with non-local regional diffusion