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−.
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