The Minimal Period Problem of Periodic Solutions for Autonomous Superquadratic Second Order Hamiltonian Systems
The Minimal Period Problem of Periodic Solutions for Autonomous Superquadratic Second Order Hamiltonian Systems
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DOI：
10.1006/jdeq.1994.1079
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发表时间：
1994-07
影响因子：
2.4
通讯作者：
Y. Long
中科院分区：
文献类型：
--
作者：
Y. Long
摘要本文研究了定义在Rn上的超二次二阶Hamilton系统在无凸性假设下具有指定最小周期的周期解的存在性.在W 1，2-偶函数空间上，我们用直接变分法解决了这个问题，并证明了新的关于莫尔斯指标的迭代不等式.利用这些工具和鞍点定理，我们得到了精确的Rabinowitz超二次条件下势函数的结果。我们证明了对任意T >0，上述系统存在一个T -周期偶解，其最小周期不小于T /（n +2）.
Abstract In this paper, we study the existence of periodic solutions with prescribed minimal period for superquadratic autonomous second order Hamiltonian systems defined on R n with no convexity assumptions. We use the direct variational approach for this problem on a W 1,2 -space of even functions, and prove new iteration inequalities on Morse indices. Using these tools and the saddle point theorem, we obtain results under precisely Rabinowitz′ superquadratic condition on potential functions. We show that for every T >0 the above mentioned system possesses a T -periodic even solution with minimal period not smaller than T /( n +2).