Infinite Dimensional Cohomology Groups and Periodic Solutions of Asymptotically Linear Hamiltonian Systems
Infinite Dimensional Cohomology Groups and Periodic Solutions of Asymptotically Linear Hamiltonian Systems
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DOI：
10.1006/jdeq.2000.3942
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发表时间：
2001-08
影响因子：
2.4
通讯作者：
A. Szulkin;W. Zou
中科院分区：
文献类型：
--
作者：
A. Szulkin;W. Zou
摘要本文研究了渐近线性Hamilton系统非平凡2π-周期解的存在性。我们认为在零和无穷远共振的情况下，我们允许时间依赖的渐近矩阵。我们的主要工具是最近由W. Kryszewski和第一作者。我们发展了一种计算新的临界群的方法。
Abstract In this paper we study the existence of nontrivial 2π-periodic solutions of asymptotically linear Hamiltonian systems. We consider the case of resonance both at zero and at infinity, and we permit time-dependent asymptotic matrices. Our main tools are an infinite dimensional cohomology theory and a corresponding Morse theory recently constructed by W. Kryszewski and the first author. We develop a method to compute the new critical groups.