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