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

We consider the nonlinear fractional problem ( - Δ ) s u + V ( x ) u = f ( x , u ) in R N We show that ground state solutions converge (along a subsequence) in L loc 2 ( R N ) , under suitable conditions on f and V , to a ground state solution of the local problem as s → 1 - .

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Bibliographic Details
Published in:Journal of fixed point theory and applications 2020, Vol.22 (3)
Main Authors: Bieganowski, Bartosz, Secchi, Simone
Format: Article
Language:English
Subjects:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Online Access:Get full text
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Description
Summary:We consider the nonlinear fractional problem ( - Δ ) s u + V ( x ) u = f ( x , u ) in R N We show that ground state solutions converge (along a subsequence) in L loc 2 ( R N ) , under suitable conditions on f and V , to a ground state solution of the local problem as s → 1 - .
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-020-00812-6