EXISTENCE AND CONCENTRATION BEHAVIOR OF GROUND STATE SOLUTIONS FOR A CLASS OF GENERALIZED QUASILINEAR SCHRODINGER EQUATIONS IN R^N  

作　　者：Jianhua CHEN Xianjiu HUANG Bitao CHENG Xianhua TANG 陈建华;黄先玖;程毕陶;唐先华(Department of Mathematics,Nanchang University,Nanchang 330031,China;School of Mathematics and Statistics,Qujing Normal University,Qujing 655011,China;School of Mathematics and Statistics,Central South University,Changsha 410083,China)

机构地区：[1]Department of Mathematics,Nanchang University,Nanchang 330031,China [2]School of Mathematics and Statistics,Qujing Normal University,Qujing 655011,China [3]School of Mathematics and Statistics,Central South University,Changsha 410083,China

出　　处：《Acta Mathematica Scientia》2020年第5期1495-1524,共30页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(11661053,11771198,11901345,11901276,11961045 and 11971485);partly by the Provincial Natural Science Foundation of Jiangxi,China(20161BAB201009 and 20181BAB201003);the Outstanding Youth Scientist Foundation Plan of Jiangxi(20171BCB23004);the Yunnan Local Colleges Applied Basic Research Projects(2017FH001-011).

摘　　要：In this article,we study the generalized quasilinear Schrodinger equation-div(ε^2g^2(u)▽u)+ε^2g(u)g′(u)|▽u|^2+V(x)u=K(x)|u|^p-2u,x∈R^N where A≥3,e>0,4<p<,22*,g∈C 1(R,R+),V∈C(R^N)∩L∞(R^N)has a positive global minimum,and K∈C(R^N)∩L∞(R^N)has a positive global maximum.By using a change of variable,we obtain the existence and concentration behavior of ground state solutions for this problem and establish a phenomenon of exponential decay.

关 键 词：generalized quasilinear Schrodinger equation ground state solutions EXISTENCE concentration behavior 

分 类 号：O175[理学—数学]