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Science China Mathematics

, Volume 61, Issue 4, pp 695–708 | Cite as

Singularly perturbed Neumann problem for fractional Schrödinger equations

  • Guoyuan Chen
Articles

Abstract

This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schrödinger equations with subcritical exponent. For some smooth bounded domain Ω ⊂ Rn, our boundary condition is given by
$$\int {\frac{{u\left( x \right) - u\left( y \right)}}{{{{\left| {x - y} \right|}^{n + 2s}}}}} dy = 0forx \in {\mathbb{R}^n} \setminus \overline \Omega $$
. We establish existence of non-negative small energy solutions, and also investigate the integrability of the solutions on Rn.

Keywords

Neumann problem nonlinear fractional Schrödinger equations singular perturbation fractional Laplacian 

MSC(2010)

35B25 35B38 35J61 

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Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11401521). The author expresses his sincere appreciation to the two anonymous referees for helpful comments and suggestions.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Data SciencesZhejiang University of Finance & EconomicsHangzhouChina

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