We show that ground state solutions to the nonlinear, fractional problem { (−∆)su + V (x)u = f(x, u) in Ω, u = 0 in RN \ Ω, on a bounded domain Ω ⊂ RN, converge (along a subsequence) in L2(Ω), under suitable conditions on f and V, to a solution of the local problem as s → 1−.

Bieganowski, B., Secchi, S. (2021). Non-local to local transition for ground states of fractional Schrödinger equations on bounded domains. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 57(2), 413-425 [10.12775/TMNA.2020.038].

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

Secchi S.
2021

Abstract

We show that ground state solutions to the nonlinear, fractional problem { (−∆)su + V (x)u = f(x, u) in Ω, u = 0 in RN \ Ω, on a bounded domain Ω ⊂ RN, converge (along a subsequence) in L2(Ω), under suitable conditions on f and V, to a solution of the local problem as s → 1−.
Articolo in rivista - Articolo scientifico
Fractional Schrödinger equation; Ground state; Nehari manifold; Non-local to local transition; Variational methods;
English
2021
57
2
413
425
partially_open
Bieganowski, B., Secchi, S. (2021). Non-local to local transition for ground states of fractional Schrödinger equations on bounded domains. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 57(2), 413-425 [10.12775/TMNA.2020.038].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/466819
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