非线性薛定谔-基尔霍夫型系统的基态解  

Ground States for a Nonlinear Schr?dinger System with Kirchhoff Term

作　　者：袁瑞银 刘艳琪[1] YUAN Ruiyin;LIU Yanqi(School of Mathematics and Physics,University of South China,Hengyang,Hunan 421001,China)

机构地区：[1]南华大学数理学院

出　　处：《南华大学学报（自然科学版）》2019年第5期68-71,共4页Journal of University of South China：Science and Technology

摘　　要：研究如下薛定谔-基尔霍夫型系统,{-(a+b∫R^3|?u1|^2dx)Δu1+λ1u 1=μ1|u1|^ 2q-2 u1+b12|u2|^q|u1|^q-2 u1,-(a+b∫R^3|?u2|^2dx)Δu2+λ2u2=μ2|u2|^2q-2 u2+b21|u1|^q|u2|^q-2 u2,u1∈H^1(R^3),u2∈H^1(R^3),其中a>0,b≥0,λi,μi(i=1,2)是任意给定的正常数,b 12=b 21>0且q∈(2,3)。分析非局部项(∫R^3|?ui|^2dx)带来的扰动影响,利用变分方法证明了系统存在一个正基态解(u1^*,u2^*),且ui^*(i=1,2)是径向对称衰减的。This paper mainly studies the existence of ground states for a coupled Schr dinger-Kirchhoff-type equations {-(a+b∫R^3|?u1|^2dx)Δu1+λ1u 1=μ1|u1|^ 2q-2 u1+b12|u2|^q|u1|^q-2 u1,-(a+b∫R^3|?u2|^2dx)Δu2+λ2u2=μ2|u2|^2q-2 u2+b21|u1|^q|u2|^q-2 u2,u1∈H^1(R^3),u2∈H^1(R^3),where a>0,b≥0,λi,μi(i=1,2)are positive constants,b 12=b 21>0 and q∈(2,3).It employs variational methods to show that the above system has at least one positive ground state(u1^*,u2^*)with ui^*,(i=1,2)radially decreasing.

关 键 词：薛定谔系统 基尔霍夫项 NEHARI流形 基态解 

分 类 号：O29[理学—应用数学]