[1]李科强.用指标理论对凸哈密顿系统周期解的一个存在性定理的推广[J].南京师大学报(自然科学版),2011,34(01):12-18.
　Li Keqiang.A Generalization of Existence of Periodic Solution of Convex Hamiltonian System by Using Ekeland Index Theory[J].Journal of Nanjing Normal University(Natural Science Edition),2011,34(01):12-18.
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用指标理论对凸哈密顿系统周期解的一个存在性定理的推广()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第34卷
期数:
2011年01期
页码:
12-18
栏目:
数学
出版日期:
2011-03-20

文章信息/Info

Title:
A Generalization of Existence of Periodic Solution of Convex Hamiltonian System by Using Ekeland Index Theory
作者:
李科强;
南京师范大学数学科学学院, 江苏南京210046
Author(s):
Li Keqiang
School of Mathematical Sciences,Nanjing Normal University,Nanjing 210046,China
关键词:
凸哈密顿系统;  周期解;  Ekeland指标;  对偶泛函
Keywords:
convex H am ilton system s;  period ic so lutions;  Ekeland index;  dua l functional
分类号:
O175.8
摘要:
考虑凸哈密顿系统周期解的存在性,利用对偶变分方法和Ekeland指标理论,得到了一个新结果,改进了Mawhin证明的哈密顿系统周期解的一个存在性定理.
Abstract:
In this paper, considering the ex istence o f pe riod ic so lutions o f convex H am ilton ian system s and utilizing the dual var iance m ethods and Eke land index theor ies, w e get a new result, w hich improv e an ex istence theorem, proved by M aw hin J the ex istence theory o f period ic so lutions o f convex H am ilton ian system.

参考文献/References:

[ 1] Eke land I. Une theo rie deM orse pour les systemes ham ilton iens convex es[ J]. Ann IH P Ana lyse Non L ineaire, 1984, 1: 19- 78.
[ 2] Ekeland I. Convex ity M ethods in H am ilton ianM echan ics[M ] . Berlin: Spr inger, 1990.
[ 3] Dong Y. P- index theory for linearH am ilton ian system s and mu ltip le so lutions for non linearH am ilton ian system s[ J] . Non linear ity, 2006, 19: 1 275-1 294.
[ 4] Long Y. Index Theo ry for Sym plectic PathsW ith Applica tions[M ]. B ase:l B irkh?user, 2002.
[ 5] Conley C, Zehnder E. M orse- type index theo ry for flow s and per iodic solutions for H am iltonian equa tions[ J]. Comm Pure App lM a th, 1984, 37: 207-253.
[ 6] Long Y. M aslov- type index theory, degene ra te critical po in ts, and asym ptotica lly linearH am iltonian sy stem s[ J]. Sc i Ch ina SerA33, 1990, 12: 1 409-1 419.
[ 7] Long Y. A M aslov- type index theory for symp lectic paths[ J]. TopolM ethods NonlinearAna,l 1997, 10( 1): 47-78.
[ 8] L i S, Liu J. M o rse theo ry and asympto tic linearH am ilton ian system[ J] . J D ifferentiona l Equ, 1989, 78( 1): 53-73.
[ 9] Dong D, Long Y. The itera tion form ula of theM aslove-type index theory w ith applica tions to nonlinea rH am ilton ian system s [ J]. Trans Am erM a Soc, 1997, 349( 7): 2 619-2 661.
[ 10] M awh in J, W illem M. C ritica l Point Theory and H am ilton ian System [M ] . Berlin: Spr inger, 1998.

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[1]陆志奇,吕建锋.具有双周期时滞捕食被捕食模型的周期解[J].南京师大学报(自然科学版),2010,33(02):6.
　Lu Zhiqi,Lü Jianfeng.Periodic Solutions in Perdator-Prey Model With Two Delays[J].Journal of Nanjing Normal University(Natural Science Edition),2010,33(01):6.

备注/Memo

备注/Memo:
基金项目: 国家自然科学基金( 10871095) . 通讯联系人: 李科强, 博士研究生, 研究方向: Ek eland指标和金融数学. E-mail:likeqiang000@ sina. com
更新日期/Last Update: 2013-04-11