一类非线性哈密顿系统的周期解

结合Maslov指标理论,利用环绕定理证明了一类非线性哈密顿系统的周期解的存在性,而这类哈密顿系统所对应的作用泛函可能不满足Palais-Smale条件.     

二阶离散Hamiltonian系统的多重周期解

利用变分原理和Clark定理,研究了带参数的二阶离散Hamiltonian系统的多重周期解,得到了此类方程周期解个数的下界估计.     

对称超二次二阶哈密尔顿系统的周期解

我们利用Ambrosetti-Rabinowitz对称形式的山路引理证明了给定周期T的对称超二次二阶哈密尔顿系统具有无穷多个反T/2-周期且奇的周期解.     

Periodic Solutions of Nonautonomous Second Order Hamiltonian Systems

In this paper, we develop the local linking theorem given by Li and Willein by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems （H） ü＋A（t）u＋∨V（t, u）=0, u∈R^N, t∈R. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem.     

离散哈密顿系统多个周期解的存在性

本文利用临界点理论,建立了一类离散哈密顿系统存在多个周期解的一些充分条件.     

具有次二次双偶位势的二阶哈密顿系统多重非平凡奇周期解的存在性

利用变分理论中的Clark定理,讨论了一类具有次二次双偶位势的二阶哈密顿系统(x|¨)(t)+V_x(t,x(t))=0多重非平凡奇周期解的存在性.     

Brake Subharmonic Solutions of Subquadratic Hamiltonian Systems

The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z(t) = J▽H(t, z(t)), where H(t, z) =1/2(B(t)z, z) +H(t, z),B(t) is a semipositive symmetric continuous matrix andH is unbounded and not uniformly coercive. It is proved that when the positive integers j and k satisfy the certain conditions, there exists a_j T-periodic nonconstant brake solution z_j such that z_j and z_(kj) are distinct.     

一类一阶Hamilton系统的次调和解

运用临界点理论中的极小极大方法得到一类一阶Hamilton系统的次调和解的存在性定理.     

Selfdual Variational Principles for Periodic Solutions of Hamiltonian and Other Dynamical Systems

Selfdual variational principles are introduced in order to construct solutions for Hamiltonian and other dynamical systems which satisfy a variety of linear and nonlinear boundary conditions including many of the standard ones. These principles lead to new variational proofs of the existence of parabolic flows with prescribed initial conditions, as well as periodic, anti-periodic and skew-periodic orbits of Hamiltonian systems. They are based on the theory of anti-selfdual Lagrangians developed recently in Ghoussoub (2007a Ghoussoub , N. ( 2007a ). Anti-selfdual Lagrangians: Variational resolutions of non self-adjoint equations and dissipative evolutions . AIHP-Analyse Non Linéaire 24 : 171 – 205 . [Google Scholar] b Ghoussoub , N. ( 2007b ). Anti-selfdual Hamiltonians: Variational resolution for Navier-Stokes equations and other nonlinear evolutions . Comm. Pure & Applied Math. 60 ( 5 ): 619 – 653 .[Crossref], [Web of Science ®] , [Google Scholar] c Ghoussoub , N. ( 2007c ). Selfdual partial differential systems and their variational principals . Submitted for publication . [Google Scholar]).     

一类二阶Hamilton系统的周期解

本文研究一类含非定线性项的二阶Ｈａｍｉｌｔｏｎ系统多周期解问题．在位势函数满足超二次齐次条件下，利用临界点理论中对称型越山定理，证明了系统存在无穷多个给定周期的周期解．     

带有偏差变元的广义Hamilton系统周期解的存在性

应用变分方法与Morse理论,本文讨论下面含有时滞的广义Hamilton系统的周期解,J*du-dt=g(t,u(t-r1),…,u(t-rs))其中J*是非奇异2n×2n反对称矩阵.在一定条件下,本文得到上述方程至少存在两个非平凡2π-周期解而对于一般的微分系统,本文给出其具有变分结构的判定性准则.     

一类二阶哈密尔顿系统的周期解

在(CPS)_C及(PS)_C条件下,利用Ambrosetti-Rabinowitz对称形式的山路引理,研究了一类二阶哈密尔顿保守系统在给定能量面上的无穷多个周期解的存在性问题.     

Periodic solutions with prescribed minimal period for the second order Hamiltonian systems with even potentials

In this paper, under a similar but stronger condition than that of Ambrosetti and Rabinowitz we find a T-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential for any T 〉 0; moreover, such a solution has T as its minimal period.     

固定位能的奇异Hamilton包含的守恒周期解

本文证明了奇异Hamilton包含—↑x∈ρ↓V（x）固定位能的守恒周期解的存在性。这里V:R^N\{0}→R是局部Lipschita连续函数，且在原点带有奇异性。     

随机哈密尔顿系统的周期变差解和近不变环面解

本文研究具有随机扰动的哈密顿系统的重现现象,尤其是轨道随机周期变差解和近不变环面解.具体来说,对线性薛定谔方程,我们完整阐述了随机周期变差解何时存在;对随机扰动的近可积哈密顿系统,我们证明了近不变环面的存在性与驱动噪声对应的哈密顿函数的对合性相关.     

Periodic Solutions of Superlinear Convex Autonomous Hamiltonian Systems

Using the Szulkin's variant of Mountain Pass Theorem, we prove the existence of nontrivial orbits with prescribed period for autonomous Hamiltonian systems in infinite dimen-sional Hilbert spaces.     

一类二阶非自治Hamilton系统的周期解

在线性增长和次线性增长条件下,利用临界点理论中的极小作用原理和鞍点定理,研究了二阶非自治Hamilton系统周期解的存在性问题,获得了一些新的可解性条件．     

Multiplicity of Periodic Solutions for Second Order Hamiltonian Systems with Asymptotically Quadratic Conditions

A class of second order non-autonomous Hamiltonian systems with asymptotically quadratic conditions is considered in this paper.Using Fountain Theorem,one multiplicity result of periodic solutions is obtained,which improves some previous results.     

双荷子系统运动的经典解

根据力学理论和经典电磁理论研究双荷子系统的运动.列出双荷子系统的运动微分方程,导出运动积分,说明系统的对称性,包括SO(4)对称性;利用变分法逆问题方法,构造双荷子系统的Lagrange(拉格朗日)函数和Hamilton(哈密顿)函数;解出双荷子系统的运动规律.