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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 14
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Research Article

Semi-classical analysis for fractional Schrödinger equations with fast decaying potentials

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Pages 5138-5155 | Received 24 Aug 2020, Accepted 26 Dec 2020, Published online: 02 Feb 2021
 

ABSTRACT

We study the following fractional Schrödinger equation ϵ2s(Δ)su+V(x)u=|u|p2u,x RN,where s(0,1), N>2s, p>1 is subcritical and V(x) is a nonnegative continuous potential. We use penalized technique and variational methods to show that the problem has a family of solutions concentrating at a local minimum of V(x) as ϵ0 provided that 2sN2+2<p<2NN2s. The novelty is that V can decay arbitrarily or even be compactly supported.

2010 Mathematics Subject Classification:

Acknowledgments

L. Duan is partially supported by China Scholarship Council (No.201906770024). Y. Peng is supported by the grant NSFC (No. 11501143).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

L. Duan is partially supported by China Scholarship Council (No. 201906770024). Y. Peng is supported by the grant National Natural Science Foundation of China (NSFC) (No. 11501143).

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