On subharmonic solutions of hamiltonian systems
On subharmonic solutions of hamiltonian systems
复制标题
DOI：
10.1002/cpa.3160330504
复制
发表时间：
1980-09
影响因子：
3
通讯作者：
P. Rabinowitz
中科院分区：
文献类型：
--
作者：
P. Rabinowitz
摘要：在文献[1]中，利用有限维极小极大变元，给出了超二次Hamilton系统（0.1）的T周期解的存在性结果，并给出了适合于传递到极限的估计.在（2）中引入了一种改进的存在机制，并将其应用于（1）中的一些超二次问题以及几种次二次问题。本文证明了这类问题不仅有一个T周期解z sub 1，而且有无穷多个不同的次调和解z sub k。在这一点上必须提出一句警告。尽管z sub k的周期为kT，但z sub k的周期可能不是最小的（即原始的）周期kT。事实上，简单的例子表明z sub k的最小周期可能存在上界。
Abstract : Some existence results for T periodic solutions of (0.1) were presented in (1) for superquadratic Hamiltonian systems using finite dimensional minimax arguments together with estimates suitable to pass to a limit. An improved existence mechanism was introduced in (2) and applied to some of the super-quadratic problems of (1) as well as to several subquadratic cases. It will show here that these problems possess not only one T periodic solutions z sub 1 but infinitely many distinct subharmonic solutions z sub k. A word of caution must be entered at this point. Although z sub k has period kT, it may not be the case that z sub k has minimal (i.e. primitive) period kT. Indeed simple examples show that there may be an upper bound on the minimal period of z sub k.