Science China Mathematics

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

Singularly perturbed Neumann problem for fractional Schrödinger equations

  • Guoyuan Chen


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.


Neumann problem nonlinear fractional Schrödinger equations singular perturbation fractional Laplacian 


35B25 35B38 35J61 


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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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© 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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