We consider the nonlinear fractional problem (-Δ)su+V(x)u=f(x,u)inRNWe show that ground state solutions converge (along a subsequence) in Lloc2(RN), under suitable conditions on f and V, to a ground state solution of the local problem as s→ 1 -.
Bieganowski, B., Secchi, S. (2020). Non-local to local transition for ground states of fractional Schrödinger equations on RN. JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS, 22(3) [10.1007/s11784-020-00812-6].
Non-local to local transition for ground states of fractional Schrödinger equations on RN
Secchi S.
2020
Abstract
We consider the nonlinear fractional problem (-Δ)su+V(x)u=f(x,u)inRNWe show that ground state solutions converge (along a subsequence) in Lloc2(RN), under suitable conditions on f and V, to a ground state solution of the local problem as s→ 1 -.
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