Non-local to local transition for ground states of fractional Schrödinger equations on bounded domains

DOI10.12775/TMNA.2020.038zbMath1477.35231arXiv1907.11455OpenAlexW3130294064MaRDI QIDQ2240525

Simone Secchi, Bartosz Bieganowski

Publication date: 4 November 2021

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.11455

zbMATH Keywords

variational methodsground stateNehari manifoldfractional Schrödinger equationnon-local to local transition

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Fractional derivatives and integrals (26A33) NLS equations (nonlinear Schrödinger equations) (35Q55) Fractional partial differential equations (35R11) PDEs on manifolds (35R01)

Related Items (3)

Small order asymptotics for nonlinear fractional problems ⋮ Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods ⋮ A Bourgain-Brezis-Mironescu formula for anisotropic fractional Sobolev spaces and applications to anisotropic fractional differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Hitchhiker's guide to the fractional Sobolev spaces
• Turbulence and diffusion. Scaling versus equations
• Ground state solutions for some indefinite variational problems
• Best constants for Sobolev inequalities for higher order fractional derivatives
• The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets
• Nonlinear Schrödinger equations with sum of periodic and vanishing potentials and sign-changing nonlinearities
• Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting
• Nonlinear Diffusion with Fractional Laplacian Operators
• Nonlocal Operators with Applications to Image Processing
• Variational Methods for Nonlocal Fractional Problems
• The Poisson equation from non-local to local
• On the Convergence in $H^1$-Norm for the Fractional Laplacian

This page was built for publication: Non-local to local transition for ground states of fractional Schrödinger equations on bounded domains