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This paper is concerned with a Neumann type problem for singularly perturbedfractional nonlinear Schr\"odinger equations with subcritical exponent. Forsome smooth bounded domain $\Omega\subset \mathbf R^n$, our boundary conditionis given by \begin{equation*}\int_{\Omega}\frac{u(x)-u(y)}{|x-y|^{n+2s}}dy=0\quad\mbox{for }x\in \mathbfR^n\setminus\bar\Omega. \end{equation*} We establish existence of nonnegativesmall energy solutions, and also investigate the integrability of the solutionson $\mathbf R^n$.

Singularly perturbed Neumann problem for fractional Schr\"odinger equations