四阶非线性周期系统周期解的存在唯一性

本文利用Liapunov函数方法,研究了一类具有缓变系数的四阶非线性非自治周期系统的周期解的存在唯一性及其渐近稳定性.我们得到了保证这些系统存在唯一稳定周期解的充分条件,并对系数的缓变范围作了较为精确的估计.     

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.     

Periodic Solutions of Second Order Superlinear Singular Dynamical Systems

We study the existence of periodic solutions of second order superlinear dynamical systems with a singularity of repulsive type. The proof is based on a well-known fixed point theorem for completely continuous operators. We do not need to consider so-called strong force conditions. Recent results in the literature are generalized and significantly improved.     

Existence of Solutions and of Multiple Solutions for Nonlinear Nonsmooth Periodic Systems

In this paper we examine nonlinear periodic systems driven by the vectorial p-Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the sublinear problem. For the semilinear problem (i.e. p = 2) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem for the superlinear problem. Our work generalizes some recent results of Tang (PAMS 126(1998)).     

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]).     

Multiplicity of Positive Periodic Solutions to Second Order Singular Dynamical Systems

The existence and multiplicity of non-collision periodic solutions for second order singular dynamical systems are discussed in this paper. Using the Green’s function of linear differential equation, we consider general singularity and do not need any kind of strong force condition. The proof relies on a nonlinear alternative principle of Leray–Schauder and a fixed point theorem in cones.     

一类非线性系统周期解的存在唯一性

运用Liapunov函数方法,研究了一类四阶非线性系统,得到了该非线性系统存在唯一渐近稳定的周期解的充分条件.     

Periodic Solutions for Nonlinear Diferential Equations

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一类非线性周期种群系统的最优收获控制

研究一类具有周期系数和年龄结构的生物动力系统的最优收获问题．应用冻结系数法和不动点原理讨论了状态系统的适定性．借助法锥概念得到了控制问题的Pontryagin极值原理，推广了文献中的一个结果．     

二阶非线性系统概周期解的存在性

该文研究某些二阶非线性系统, 利用平均法给出了非线性系统概周期解存在性的某些充分条件, 推广了已知结果. 二个特殊系统用于说明其结果的可行性和更一般性.     

海-气耦合气候系统非线性扰动模式的周期正解

与ENSO相关的热带大尺度海-气相互作用是影响全球气候年际变化的主要过程之一.该文从一个海-气相互作用方程组出发,推广了一个具有一般形式的海 气耦合气候系统非线性扰动模式.运用拓扑度理论,从数学上严格证明了一定条件下该模式存在周期正解的结果,并分析了所得结果潜在的应用价值.海-气相互作用研究,有助于理解气候变化过程,为气候模拟和预报提供理论基础.     

在共振点的一阶微分系统的周期解

考虑具偏差变元的一阶非线性微分系统:x>(t)=Bx(t)+F(x(t-τ))+p(t),其中,x(t)∈R2,τ∈R,B∈R2×2,F是有界的,p(t)是连续的2π-周期函数.应用Brouwer度及Mawhin重合度理论,在共振的情况下,给出了上述方程存在2π-周期解的充分条件及其在Duffing方程上的应用.     

非线性差分方程的多重周期解

用变分方法得到一类非线性差分方程多重周期解的存在性．我们的结果推广了Cai，Yu和Guo[Comput．Math．Appl．，52（2006），1630-1647]的结果，并且这里给出的证明显著地简化了．     

Existence of Small Periodic Solutions of Nonlinear Systems of Ordinary Differential Equations

We investigate the case where conditions for the existence of a nonzero periodic solution of a system of ordinary differential equations are determined by the properties of elements of the matrix of linear approximation and the properties of nonlinear terms.     

一类单种群系统正周期解及其稳定性

考虑周期单种群模型 dxdt=xg( t,x)± p( t,x)的正周解及其稳定性 .证明了在一定条件下 ,系统存在全局吸引的正周期解 .给出了系统存在两个正周期解的充分条件 ,同时也给出了种群灭绝的条件 .这些结果用于 Logistic模型和 Odum模型 ,得到了被开发的周期 Logistic模型存在全局吸引的正周期解 ;被开发了的周期 Odum模型只存在两个正周期解 ,其中之一吸引初值大于一个定数的所有解 ,另一个周期解则是种群灭绝的分界线