Non-local to local transition for ground states of fractional Schrödinger equations on ${\mathbb{R}}^N$

Abstract

We consider the nonlinear fractional problem \begin{align*} (-Δ)^{s} u + V(x) u = f(x,u) &\quad \hbox{in ${\mathbb{R}}^N$} \end{align*} We show that ground state solutions converge (along a subsequence) in $L_{\mathrm{loc}}^2({\mathbb{R}}^N)$, under suitable conditions on $f$ and $V$, to a weak solution of the local problem as $s\to 1^{-}$.

arXiv admin note: text overlap with arXiv:1907.11455

References in corpus (4)

• Nonlinear Schrödinger equations with sum of periodic and vanishing potentials and sign-changing nonlinearities
• The Poisson equation from non-local to local
• Solutions of the fractional Schrödinger equation with sign-changing nonlinearity
• Non-local to local transition for ground states of fractional Schrödinger equations on bounded domains