Kirchhoff型分数阶Hamiltonian系统基态解的存在性和集中性  

Existence and concentration of ground state solutions for Kirchhoff-type fractional Hamiltonian systems

作　　者：薛婷婷[1] 曹虹[1] 姜永胜[1] 刘元彬 XUE Ting-ting;CAO Hong;JIANG Yong-sheng;LIU Yuan-bin(School of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830000,Xinjiang,China)

机构地区：[1]新疆工程学院数理学院,新疆乌鲁木齐830000

出　　处：《云南大学学报（自然科学版）》2022年第6期1107-1117,共11页Journal of Yunnan University(Natural Sciences Edition)

基　　金：新疆维吾尔自治区科技厅青年科学基金(2021D01B35);新疆维吾尔自治区高校科研计划自然科学项目(XJEDU2021Y048);新疆工程学院博士启动基金(2020xgy012302).

摘　　要：研究一类Kirchhoff型分数阶Hamiltonian系统基态解的存在性和渐近行为.通过构造合适的分数阶空间,在对称矩阵L(t)满足半正定的条件下,给出新的嵌入定理及几个重要的不等式,利用临界点理论,得到上述系统基态解的存在性和集中性结果.We study the existence and asymptotic behavior of ground state solutions for a class of Kirchhoff-type fractional Hamiltonian systems.By constructing a suitable fractional space,under the condition that the symmetric matrix L(t)satisfies the positive semi-definite condition,a new embedding theorem and several important inequalities are given.Using the critical point theory,the existence and concentration results of the ground state solution of the above system are obtained.

关 键 词：Kirchhoff型方程 分数阶Hamiltonian系统 Nehari流形方法 基态解 集中性. 

分 类 号：O175.14[理学—数学] O175.8[理学—基础数学]