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Singularly perturbed Neumann problem for fractional Schrödinger equations (1409.4556v4)
Published 16 Sep 2014 in math.AP
Abstract: 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 $\Omega\subset \mathbf Rn$, 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 Rn\setminus\bar\Omega. \end{equation*} We establish existence of nonnegative small energy solutions, and also investigate the integrability of the solutions on $\mathbf Rn$.