二阶非线性微分方程零解的全局渐近稳定性

本文研究了具有四个非线性项零解的全局渐近稳定性。     

The Global Smooth Solution for Landau-Lifshitz-Maxwell Equation Without Dissipation

In this paper, the global existence of a unique smooth solution for the Landau-Lifshitz-Maxwell equations of the ferromagnetic spin chain without dissipation in n (1 ≤ n ≤ 2) dimensions is established by using the viscosity elimination method.     

具时滞的Hopfield网络周期解的指数稳定性

The paper is devoted to periodic attractor of delayed Hopfield neural networks with time-varying.By constructing Lyapunov functionals and using inequality techniques,some new sufficient criteria are obtained to guarantee the existence and global exponential stability of periodic attractor.Our results improve and extend some existing ones in[13～14].One example is also worked out to demonstrate the advantages of our results.     

具分片常变量泛函微分方程的全局稳定性

本文研究具分片常变量泛函微分方程,其中[·]表示取整函数,r(t)∈C([0,+c),(0,+c)),P_i∈[0,+c),(i=1,2,…,m),P_m>0,文中给出了保证方程的每一满足初始条件N(0)=N₀>0,N(-j)=N_-j≥0(j=1,2,…,m),的解N(t)满足lim_t→∞N(t)=N^*的一些新的充分条件.     

一类拟线性波方程的整体光滑解

In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxtt=β(uxn)x, where k>0 and βare real numbers, and n≥2 is an integer. We prove that for any T>0, the Cauchy problem admits a unique global smooth solution u ∈C∞((0, T); H∞(R))∩C ([0, T]; H2(R))∩C1([0, T]; L2(R)) under suitable assumptions on the initial data.     

具有避难所的非自治竞争系统的持续生存和全局稳定性

考虑一个四缀块模型，其中一缀块里有三个竞争种群，另外三个分别是它们的避难所，并且种群能在竞争缀块和各自的避难所间相互扩散．在一定的条件下，我们给出了此模型的持续生存，周期性和全局稳定性．     

广义Kuramoto-Sivashinsky方程强解的全局吸引子的存在性

Using a new method developed in[5],we prove the existence of global attractors for the Generalized Kuramoto-Sivashinsky equation in H3per(Ω)and H4per(Ω).     

无限真空中有外力的Enskog方程整体解

首先给出对应于带有外力的Enskog方程的次特征方程组的假设.由于Enskog方程的碰撞算子比Boltzmann方程的复杂,所以这些假设比Duan等人就Boltzmann方程给出的复杂.这些假设与中等或更稠密的气体的粒子碰撞有着密切的关系,而且用它们来估计Enskog积分方程中所谓的获得和损失积分.接着,通过控制这些积分,证明用于描述无限真空中中等或更稠密的气体的Enskog方程整体温和解存在唯一.最后,对Enskog方程中碰撞因子的局部Lipschitz假设作些注释.     

一类耗散的Hasegawa-Mima方程的整体解

Applying the integral a priori estimates method, the existence and uniqueness of the global solution for the dissipative Hasegawa-Mima equation with initial periodic boundary condition was proved.     

一类非线性微分方程周期解及全局稳定性

本文研究下面一类非线性微分方程dsdt=1 -s- x1 s0 δQ2 ( m1 s0 sk1 s0 s-k)dx1 dt =x1 Q( m1 s0 sk1 s0 s-k) -x1 -x2m2 x1 /Qk2 x1 /Qdx2dt =x2Qm2 x1 /Qk2 x1 /Q -x2　　如果条件m2 x 2 (k1 δ s0 δ-Qλ2 -x 2 ) 2 >m1 δk1 (k2 Q2 λ2 ) 2成立时 ,系统在Ω内存在周期解 ;如果条件m2 x 2 (k1 δ s0 δ -Qλ2 -x 2 ) 2 相似文献   

A Branching Method for Studying Stability of a Solution to a Delay Differential Equation

We study stability of antisymmetric periodic solutions to delay differential equations. We introduce a one-parameter family of periodic solutions to a special system of ordinary differential equations with a variable period. Conditions for stability of an antisymmetric periodic solution to a delay differential equation are stated in terms of this period function.     

时滞差分方程零解的全局渐近稳定性

The difference equation△x_n p_nx_(n-k)=f(n,x_(n-11),…,x_(n-1m),n= 0,1,2,…is considered,where{Pn}is a sequence of nonnegative real numbers,m∈{1,2,,…),k,l_1,…,l_m∈{0,1,2,,…}.Some sufficient conditions for the global asymp- totic stability of zero solution of the equation are obtained.     

一类耦合非线性波动方程全局解的存在性

利用微分不等式和解的延拓原理,研究了一类带非线性阻尼和源项的耦合非线性波动方程,通过分析方程中参数的关系,得到了全局解存在的一些新的充分条件.     

一类非线性广义Euler-Poisson-Darboux方程整体解的渐近性质

J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.     

具有时滞及B-D功能反应的食物链系统周期解的存在性与全局渐近稳定性

研究了具有时滞和Beddington-DeAngelis功能反应的一类食物链系统,通过运用Mawhin重合度理论中的延拓定理,得到了系统至少存在一个周期解的充分条件,并通过构造Lyapunov泛函的方法得到了系统周期解的全局稳定性.     

具有概周期系数的三种群第Ⅱ类功能性反应的全局渐近稳定性

讨论了一类具有概周期系数的三种群第Ⅱ类功能性反应的模型，通过利用微分不等式及构造适当的李雅普诺夫函数获得了其存在全局渐近稳定性的概周期解的充分条件．     

Global Existence with Large Data for a Nonlinear Weakly Hyperbolic Equation

We prove a global existence result for a semilinear degenerate hyperbolic Cauchyproblem with large data, in the case ofa subcritical defocusing power nonlinearity, in 1 and 2 space dimensions.     

Existence of Infinite Energy Solution to the Inelastic Boltzmann Equation with External Force

In this paper, the Cauchy problem for the inelastic Boltzmann equation with external force is considered in the case of initial data with infinite energy. More precisely, under the assumptions on the bicharacteristic generated by external force, we prove the global existence of solution for small initial data compared to the local Maxwellian exp{–p|x – v|²}, which has infinite mass and energy.     

带外力的Enskog方程

本文在初值对时间变量和空间变量都具有多项式衰减时,证明了带外力Ens-kog方程解的存在性和唯一性.     

广义Hasegawa-Mima方程整体解的存在惟一性

运用关于时间的一致先验估计,证明了具有周期边值条件的广义Hasegawa-Mima方程整体解的存在性、惟一性.