Non-local to local transition for ground states of fractional Schrödinger equations on $$\mathbb {R}^N$$
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Abstract We consider the nonlinear fractional problem $$\begin{aligned} (-\Delta )^{s} u + V(x) u = f(x,u)&\quad \hbox {in } \mathbb {R}^N \end{aligned}$$ ( - Δ ) s u + V ( x ) u = f ( x , u ) in R N We show that ground state solutions converge (along a subsequence) in $$L^2_{\mathrm {loc}} (\mathbb {R}^N)$$ L loc 2 ( R N ) , under suitable conditions on f and V, to a ground state solution of the local problem as $$s \rightarrow 1^-$$ s → 1 - .
2014 ◽
Vol 58
(2)
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pp. 305-321
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2013 ◽
Vol 54
(3)
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pp. 031501
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2017 ◽
Vol 97
(7)
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pp. 1154-1171
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2012 ◽
Vol 142
(4)
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pp. 867-895
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2016 ◽
Vol 71
(4)
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pp. 965-976
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2010 ◽
Vol 53
(2)
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pp. 245-255
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