一类具有超线性项的Kirchhoff方程的变号解  

Existence of Sign-Changing Solutions for Kirchhoff Type Equation with Superliner Nonlinearity

作　　者：张玲[1] 吕颖[1] ZHANG Ling;LÜYing(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2022年第6期34-40,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11601438).

摘　　要：研究了一类Kirchhoff方程-a+b∫R^(3)|■u|2dxΔu+V(x)u=f(u)x∈R^(3)其中a,b>0,位势函数V具有双位势阱,f满足一类超三线性增长条件.通过变分法,证明了最小能量变号解的存在性.In the present paper,the following Kirchhoff type equation-a+b∫R^(3)|■u|2dxΔu+V(x)u=f(u)x∈R^(3)has been considered,where a,b>0 and the potential V has double potential well,with a superliner nonlinearity f.With the help of the variational method,the existence of least energy sign-changing solutions has been shown.

关 键 词：KIRCHHOFF方程 变分法 变号解 

分 类 号：O176.3[理学—数学]