一类二阶离散哈密顿系统多个周期解的存在性

Existence of multiple periodic solutions for a class of second-order discrete Hamiltonian systems

利用临界点理论,引入一类控制函数,得到一些新的多解性条件,借助这些条件研究具有局部周期位势的二阶离散哈密顿系统多个周期解的存在性问题,所得结果不同于已有文献中的结论。

Based on the critical point theory, a kind of control function is introduced, and some new mul- tiple solution conditions are obtained. Thereby, the multiplicity of periodic solutions for a class of second- order discrete Hamihonian systems with partially periodic potentials is studied. The obtained results are different from thoses in literatures.