Normalized solutions for the fractional NLS with mass supercritical nonlinearity

Luigi Appolloni; Simone Secchi

Normalized solutions for the fractional NLS with mass supercritical nonlinearity

Analysis of PDEs 2020-11-09 v2

Authors: Luigi Appolloni , Simone Secchi

Abstract

We investigate the existence of solutions to the fractional nonlinear Schr\"{o}dinger equation $(-\Delta)^s u = f(u)$ with prescribed $L^2$ -norm $\int_{\mathbb{R}^N} |u|^2 \, dx =m$ in the Sobolev space $H^s(\mathbb{R}^N)$ . Under fairly general assumptions on the nonlinearity $f$ , we prove the existence of a ground state solution and a multiplicity result in the radially symmetric case.

Keywords

nonlinear schrödinger equations nonlinear schrodinger equations semilinear elliptic equations

Cite

@article{arxiv.2006.00239,
  title  = {Normalized solutions for the fractional NLS with mass supercritical nonlinearity},
  author = {Luigi Appolloni and Simone Secchi},
  journal= {arXiv preprint arXiv:2006.00239},
  year   = {2020}
}

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