带诺依曼边界的非局部问题非平凡解的存在性

摘要

主要考虑一类带诺依曼边界的分数阶薛定谔方程的非平凡解的存在性，通过直接计算我们得到非局部算子的分部积分公式和格林公式。该问题具有变分结构。通过验证该问题满足山路引理条件，证明了该问题存在非平凡解的结论。%The main purpose of this paper is to investigate the existence of nontrivial solution of a Neumann type problem for fractional Schrodinger equations.Through direct computation, we obtain the integration by parts formula and Green′s identity. The problem has a variational structure.Through verifying the problem satisfying the Mountain pass theorem, we prove the existence of nontrivial solution of this problem.