分数阶Schr?dinger方程的非平凡解的存在性

The existence of nontrivial solution of the nonlinear fractional Schr?dinger equation

考虑了以下分数阶Schr?dinger方程{(-Δ)su+V(x)u=|u|^(p-2)u,x∈R^N,u∈Hs(R^N),的非平凡解的存在性,其中2<p<2*(s)=2N/N-2s,N>2s,0<s<1,位势函数V(x)连续且满足一定条件.运用山路引理得到了相关结果.

The paper considered the existence of nontrivial solution of the following fractional Schrodinger equation-Δ^su+V(x)u=∣u∣^p-2 u,x∈R^N,u∈H^s(R^N),where 2<p<2*(s)=2N/N-2s,N>2s,0<s<1,and the potential V(x)satisfies certain conditions.We mainly use the mountain pass theorem to obtain the result in this paper.