Singularly perturbed Neumann problem for fractional Schrdinger equations

This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schrdinger equations with subcritical exponent. For some smooth bounded domain ?  R~n, our boundary condition is given by∫?u(x)-u(y)/|x-y|n+2sdy = 0 for x ∈ R~n\?.We establish existence of non-negative small energy solutions, and also investigate the integrability of the solutions on Rn.