Ground state solutions for nonlinear fractional Schrödinger equations in \mathbb R^NRN

2012/08/31 by Simone Secchi · 1 citation
Materials Science · Mathematics · #Class (philosophy) #Construct (python library) #Geometric Analysis and Curvature Flows #Ground state #Minification #Nonlinear Partial Differential Equations #Nonlinear system #Nonlocal and gradient elasticity in micro/nano structures #State (computer science) #Variational analysis #Variational method #math.AP #msc:35A15 #msc:35J20 #msc:35Q55

paper · pdf · doi:10.1063/1.4793990

17 pages

arxiv created 2013/01/28 · openalex publication_date 2013/03/01 · arxiv updated 2015/06/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We construct solutions to a class of Schrödinger equations involving the fractional Laplacian. Our approach is variational in nature, and based on minimization on the Nehari manifold.

Citations

• The Pohozaev Identity for the Fractional Laplacian
• Fractional Schrödinger equation
• Hitchhikerʼs guide to the fractional Sobolev spaces
• Regularity of the obstacle problem for a fractional power of the laplace operator

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• Concentration phenomena for a fractional Schrödinger‐Kirchhoff type equation