Existence and Concentration of Solutions for An Indefinite Schrodinger-Kirchhoff System  

一类不确定薛定谔基尔霍夫方程解的存在性和集中性

作　　者：CHEN Yu-song CHANG He-jie 陈玉松;常荷洁(Ministry of Basic Education,Shangqiu Institute of Technology,Henan Shangqiu 476300,China;Ministry of Basic Education,Luohe Vocational Technology College,Henan Luohe 462000,China)

机构地区：[1]Ministry of Basic Education,Shangqiu Institute of Technology,Henan Shangqiu 476300,China [2]Ministry of Basic Education,Luohe Vocational Technology College,Henan Luohe 462000,China

出　　处：《Chinese Quarterly Journal of Mathematics》2020年第1期37-45,共9页数学季刊（英文版）

基　　金：Supported by the Youth Foundation of Shangqiu Institute of Technology(2018XKQ01)。

摘　　要：This paper is concerned with the nonlinear Schrodinger-Kirchhoff system-(a+b∫R^3/u/^2dx)△u+λV(x)u=f(x,u)in R^3,where constants a>0,6≥0 andλ>0 is a parameter.We require that V(x)∈C(R^3)and has a potential well V^-1(0).Combining this with other suitable assumptions on K and f,the existence of nontrivial solutions is obtained via variational methods.Furthermore,the concentration behavior of the nontrivial solution is also explored on the set V^-1(0)asλ→+∞as A—>H-oo as well.It is worth noting that the(PS)-condition can not be directly got as done in the literature,which makes the problem more complicated.To overcome this difficulty,we adopt different method.

关 键 词：Schrodinger-Kirchhoff SYSTEM SUBLINEAR Variational methods CONCENTRATION 

分 类 号：O177.92[理学—数学]