Singularly perturbed Neumann problem for fractional Schrödinger equations

This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schrödinger equations with subcritical exponent. For some smooth bounded domain Ω ⊂ R n , our boundary condition is given by ∫ u ( x ) − u ( y ) | x − y | n + 2 s d y = 0 f o r x ∈ ℝ n ∖ Ω ¯ . We establish existence of non-negative small energy solutions, and also investigate the integrability of the solutions on R n .