Singularly perturbed Neumann problem for fractional Schrödinger equations

Abstract

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

17 pages. References updated

References in corpus (2)

• Concentration phenomenon for fractional nonlinear Schrödinger equations
• Multiple Semiclassical Standing Waves for Fractional Nonlinear Schrödinger Equations

Cited by in corpus (1)

• Multiplicity of solutions for a class of fractional elliptic problem with critical exponential growth and nonlocal Neumann condition