摘要
该文考虑了如下薛定谔方程{-△u+V(x)u=f(x,u),对x∈R^N,u(x)→0,当|x|→∞,其中V与f关于x是周期的,0是谱σ(-△+V)的一个边界点.受最近的文献[35]的启发,进一步考虑了f(x,u)在|u|→∞时是渐近线性的情况,并利用非Nehari流形方法得到了该方程的基态解.与广义Nehari流形方法相比,该方法更加简便、直接.
This paper is concerned with the following Schrodinger equation {-△u+V(x)u=f(x,u),对x∈R^N,u(x)→0,当|x|→∞ where V and f are both periodic in x and 0 is a boundary point of the spectrum σ(-△+V). Inspired by recent work of Tang[35], we consider further the case that f(x, u) is asymptotically linear as |u|→∞, and obtain the existence of ground state solutions using the non-Nehari manifold method which is more direct and simpler than the generalized manifold method.
出处
《数学物理学报(A辑)》
CSCD
北大核心
2016年第6期1103-1116,共14页
Acta Mathematica Scientia
基金
国家自然科学基金(11571370
11471278
11471137)
湖南省研究生科研创新项目(CX2015B037)
国家留学基金委(201506370092)
高等学校博士学科点专项科研基金(20120162110021)资助~~
关键词
薛定谔方程
渐近线性
非Nehari流形方法
谱点零
基态解
SchrSdinger equation
Asymptotically linear
Spectrum point zero
Non-Nehari manifold method
Ground states solutions.