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arXiv · 1911.08570

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

Bartosz Bieganowski·Simone Secchi
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Abstract

We consider the nonlinear fractional problem \begin{align*} (-\Delta)^{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 $L^2_{\mathrm{loc}} (\mathbb{R}^N)$, under suitable conditions on $f$ and $V$, to a weak solution of the local problem as $s \to 1^-$.

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Bartosz Bieganowski, Simone Secchi. 2019-11-18. Non-local to local transition for ground states of fractional Schr\"{o}dinger equations on $\mathbb{R}^N$. https://doi.org/10.1007/s11784-020-00812-6

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