分数阶Hamiltonian系统的可解性  

Solvability of fractional Hamiltonian systems

作　　者：薛婷婷[1] XUE Ting-ting(School of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830023,Xinjiang,China)

机构地区：[1]新疆工程学院数理学院,新疆乌鲁木齐830023

出　　处：《云南大学学报（自然科学版）》2023年第6期1179-1188,共10页Journal of Yunnan University(Natural Sciences Edition)

基　　金：新疆维吾尔自治区青年科学基金(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：研究一类分数阶Hamiltonian系统解的存在性.考虑含有参数的势函数W(t,u)满足新的超线性和次线性组合条件W(t,u)=W_(1)(t,u)+μW_(2)(t,u),μ>0.当|u|→∞时,W_(1)(t,u)满足更一般的超线性增长条件,代替Ambrosetti-Rabinowitz条件;W_(2)(t,u)满足更一般的次线性增长条件.这部分需要建立新的紧嵌入定理,用于验证序列的紧性.利用临界点理论,得到上述系统2个解存在结果.We study the existence of solutions for fractional Hamiltonian systems.We consider the potential function W(t,u)with parameters to satisfy the new superlinear and sublinear combination conditions W(t,u)=W_(1)(t,u)+μW_(2)(t,u),μ>0 When|u|→∞,W_(1)(t,u)satisfies the more general superlinear growth conditions,instead of the Ambrosetti-Rabinowitz condition;W_(2)(t,u)satisfies more general sublinear growth conditions.In this part,we need to establish a new compact embedding theorem to verify the compactness of the sequence.Using the critical point theory,the existence results of two solutions of the above system are obtained.

关 键 词：分数阶微分方程 HAMILTONIAN系统 变分方法 解的存在性. 

分 类 号：O175.14[理学—数学] O175.8[理学—基础数学]