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1.
一类非自治非线性微分方程周期解的存在性   总被引:3,自引:0,他引:3  
本文讨论非自治非线性微分方程组■=ф(y)-f(x),■=-g(x)+e(t) (1)周期解的存在性.N.Levinson 曾给出■(y)≡y、g(x)≡x 时系统(1)存在周期解的条件,井竹君推广了文[1]的工作.本文给出方程组(1)存在周期解的一组充分条件,进一步推广了文[2]的结果.  相似文献   

2.
何莲花  刘安平 《数学杂志》2012,32(5):825-831
本文在Banach空间PC(J)上研究了一阶脉冲微分方程的周期解.利用迭代分析法得到了一阶脉冲微分方程周期解的存在唯一性和其解在Banach空间PC(J)上的范数估计.  相似文献   

3.
广义Liénard方程非平凡周期解的存在性   总被引:2,自引:0,他引:2  
本文讨论广义Linard方程x f(x)φ(x)x g(x)η(x)=0非平凡周期解的存在性,所获结果推广并改进了一些现有的关于Linard方程周期解的存在性定理。  相似文献   

4.
一类二阶泛函微分方程周期解存在性问题   总被引:18,自引:0,他引:18  
任景莉  葛渭高 《数学学报》2004,47(3):569-578
利用重合度理论研究一类二阶泛函微分方程x″(t)+f(t,x_t)x′~n+β(t)g(x(t-τ(t)))=p(t)的周期解问题,本文得到了周期解存在的新的结果。  相似文献   

5.
为了得到干摩擦问题存在周期解的判断方法,利用微分包含理论对系统+k~2x+μSngp(t)+T(t)a.e.进行了讨论.在周期外力p(t)周期等于固有周期2π/R的情形下得到了周期解存在的充要条件,在周期外力p(t)周期不等于固有周期整数倍2nπ/R的情形下得到了周期解存在的充分条件.  相似文献   

6.
利用Fourier级数理论和重合度理论研究了一类二阶n-维中立型泛函微分系统d2/dt2(x(t)-Cx(t-r))+d/dt gradF(x(t))+gradG(x(t-τ(t)))=p(t)的周期解问题,得到了周期解存在性的新结论,有意义的是本文的矩阵C仅为一般的实方阵,不必为实对称阵,因而本文的结果改进和推广了已有工作.此外,本文周期解先验界估计方法与已有工作也不同.  相似文献   

7.
本文利用扩展的F-展开法,针对耦合Schr(o)dinger-Boussinesq方程组,求得了一系列完善的精确解,包含了周期波解、三角函数解、有理函数解.  相似文献   

8.
]文 [1 ]给出了一类具两个滞量的方程存在周期解的充分条件 ,但并没有给出周期解的表达式 .本文给出了方程 x( t) =-x t-π3 3-x t-2π3 3周期解的部分表达式 .  相似文献   

9.
李林 《大学数学》2001,17(6):23-28
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  相似文献   

10.
非临界情形下发展方程的周期解   总被引:1,自引:0,他引:1  
李永祥 《数学季刊》1992,7(2):103-104
考虑抽象发展方程周期问题: 这里,A(t)(t∈R)为Banach空间X中的稠定闭线性算子,满足Sobolevskii条件,A(0)有紧连续的逆算子。记X_α(0≤α≤1)为由A(0)确定的内插空间。称周期问题(1)或(2)是非临界的,如果相应的线性齐次方程没有非零ω-周期解。对线性非齐问题(1),文[3]在A(t)≡A这种半自治情形,获得了周期解的存在性。我们  相似文献   

11.
冯学尚  邵琨 《应用数学》1994,7(2):230-234
本文讨论由Ott E.等建立的机械模型,并给出了该模型初值问题存在整体性弱解的证明。  相似文献   

12.
本文通过建立通解矩阵的概念 ,给出了用初等行变换求线性矩阵方程 Am× n Xn× s=Bm× s的通解的方法 .  相似文献   

13.
This paper is concerned with a class of neutral difference equations of second order with positive and negative coefficients of the forms
where τ, δ and σ are nonnegative integers and {p n }, {q n } and {c n } are nonnegative real sequences. Sufficient conditions for oscillation of the equations are obtained. Research of the first author was supported by Department of Science and Technology, New Delhi, Govt. of India, under BOYSCAST Programme vide Sanc. No. 100/IFD/5071/2004-2005 Dated 04.01.2005.  相似文献   

14.
Sufficient conditions have been obtained for the existence of at least two non-negative periodic solutions to a system of first-order nonlinear functional differential equations. Applications to some ecological models are given.  相似文献   

15.
16.
In this paper, we study the traveling wave solutions for a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrodinger (NLS) equation in the ultrashort-pulse regime. The corresponding traveling wave systems of the equivalent complex short-pulse equations are two singular planar dynamical systems with four singular straight lines. By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions.  相似文献   

17.
Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived.  相似文献   

18.
We show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term Δu+|∇u|=p(|x|)f(u,v), Δv+|∇v|=q(|x|)g(u,v) on RN, N?3, provided that nonlinearities f and g are positive and continuous, the potentials p and q are continuous, c-positive and satisfy appropriate growth conditions at infinity. We find that entire large positive solutions fail to exist if f and g are sublinear and p and q have fast decay at infinity, while if f and g satisfy some growth conditions at infinity, and p, q are of slow decay or fast decay at infinity, then the system has infinitely many entire solutions, which are large or bounded.  相似文献   

19.
In this paper, we study the solvability of the operator equations in the general setting of infinite-dimensional Hilbert space with corresponding operators no necessarily having closed range. We get the necessary and sufficient conditions for the existences of the solutions and obtain formulae in each case for the general selfadjoint, positive and real positive solutions to these operator systems.  相似文献   

20.
In this paper, a class of discrete-time backward non-linear equations defined on some ordered Hilbert spaces of symmetric matrices is considered. The problem of the existence of some global solutions is investigated. The class of considered discrete-time non-linear equations contains, as special cases, a great number of difference Riccati equations both from the deterministic and the stochastic framework. The results proved in the paper provide the sets of necessary and sufficient conditions that guarantee the existence of some special solutions of the considered equations as: the maximal solution, the stabilizing solution and the minimal positive semi-definite solution. These conditions are expressed in terms of the feasibility of some suitable systems of linear matrix inequalities (LMI). One shows that in the case of the equations with periodic coefficients to verify the conditions that guarantee the existence of the maximal or the stabilizing solution, we have to check the solvability of some systems of LMI with a finite number of inequations. The proofs are based on some suitable properties of discrete-time linear equations defined by the positive operators on some ordered Hilbert spaces chosen adequately. The results derived in this paper provide useful conditions that guarantee the existence of the maximal solution or the stabilizing solution for different classes of difference matrix Riccati equations involved in many problems of robust control both in the deterministic and the stochastic framework. The proofs are deterministic and are accessible to the readers less familiarized with the stochastic reasonings.  相似文献   

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