Non-local to local transition for ground states of fractional Schr\"{o}dinger equations on bounded domains
Bartosz Bieganowski, Simone Secchi · arXiv (Cornell University) · 2019
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−.