共查询到20条相似文献,搜索用时 218 毫秒
1.
In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost periodic solution for the above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the positive almost periodic solution are derived. 相似文献
2.
THE BEHAVIOR OF SOLUTIONS IN THE VICINITY OF A BOUNDED SOLUTION TO AUTONOMOUS DIFFERENTIAL EQUATIONS
Lin Guotian 《数学年刊B辑(英文版)》1986,7(2):205-212
By using the exponential dichotomy,this paper investigates the behavior of solutionsin the vicinity of a bounded solution to the autonomous differential systemdx/dt=f(x).(1)Suppose x=u(t)is a nontrivial bounded solution of system(1).By discussing theequivalent equations of system(1)dθ/dt=1 (p,θ)dp/dt=A(θ)p (p,θ)(2)with respect to the moving orthonormal transformationx=u(θ) s(θ)p,the author proves that if linear system corresponding to(2)admits exponential dichotomy,then the given bounded solution x=u(t)should be periodic.The author also discusses thestadility of the obtained periodic solution.Finally,this paper discusses perturbation of thebounded solution of autonomous system(1). 相似文献
3.
Lin Zhengsheng 《数学年刊B辑(英文版)》1984,5(3):363-373
By using the exponential dichotomy and the averaging method,a perturbation theoryis established for the almost periodic solutions of an almost differential system.Suppose that the almost periodic differential system(dx)/(dt)=f(x,t) ε~2g(x,t,ε)(1)has an almost periodic solution x=x_0(t,M)for ε=0,where M=(m_1,…,m_k)is theparameter vector.The author discusses the conditions under which(1)has an almostperiodic solution x=x(t,ε)such that x(t,ε)=x_0(t,M)holds uniformly.The results obtained are quite complete. 相似文献
4.
钱定边 《中国科学A辑(英文版)》2002,45(2):214-222
We establish the coexistence of periodic solution and unbounded solution, the infinity of largeamplitude subharmonics for asymmetric weakly nonlinear oscillator x" + a2x+ - b2x- + h(x) = p(t) with h(±∞) - 0 and xh(x) → +∞(x →∞), assuming that M(τ ) has zeros which are all simple and M(τ ) 0respectively, where M(τ ) is a function related to the piecewise linear equation x" + a2x+ - b2x- = p(t).`` 相似文献
5.
For the nonlinear schrodinger equation it_t u_(xx) 2|u|~u=0, the writer once obtained a new periodic solution (x, t). In this paper, we will discuss some properties of (x, t), get all the main spectrum and the auxiliary spectrum of (x, t), and analyse motion forms of the spectra. We will also prove that (x, t) is an one-band potential. 相似文献
6.
This paper studies the behaviors of the solutions in the vicinity of a givenalmost periodic solution of the autonomous system
x′=f(x), x Rn , (1)
where f C1 (Rn ,Rn ). Since the periodic solutions of the autonomous system are not Liapunov asymptotic stable, we consider the weak orbitally stability.
For the planar autonomous systems (n=2), the classical result of orbitally stability about its periodic solution with period w belongs to Poincare, i.e. 相似文献
7.
In this paper, we study the Logistic type equation x= a(t)x -b(t)x^2+ e(t). Under the assumptions that e(t) is small enough and a(t), b(t) are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a(t), b(t) and e(t) are periodic functions, and this solution is an almost periodic solution if a(t), b(t) and e(t) are almost periodic functions. 相似文献
8.
1 IntroductionConsider equation of the Duffing fOrmX" cx' g(x) = p(t) (1)where c is a constant, p and g are continuous functions defined on (--oo, oc).In the early years of the l990's, some authors investigated the existence andstability of periodic solution of system (1), when p(t) is a periodic function(see [1],[2]).In this paper, we consider the situation in where p(t) is an almost periodicfunction. Under some conditions, we prove the existence and uniqueness ofalmost periodic soluti… 相似文献
9.
By using the theory of coincidence degree,we study a kind of periodic solutions to second order differential equation with a deviating argument such as x"(t) f(x'(t)) h(x(t))x'(t) g(x(t-τ(t)))=p(t),some sufficient conditions on the existence of periodic solutions are obtained. 相似文献
10.
陈国旺 《数学物理学报(B辑英文版)》1991,(4)
In this paper, the periodic boundary problem and the initial value problem for the nonlinear system of parabolic type u_1=-A(x, t)u_(x4)+B(x, t)u_(x2)+(g(u))_(x2)+(grad h(u))_x+f(u)are studied, where u(x, t)=(u_1(x, t).…, u_J(x, t) is a J-dimensional unknown vector valued function, f(u) and g(u) are the J-dimensional vector valued function of u(x, t), h(u) is a scalar function of u, A(x, t) and B(x, t) are J×J matrices of functions. The existent, uniqueness and regularities of the generalized global solution and classical global solution of the problems are proved. When J=1, h(u)=0, g(u)=au~3, A=a_1, B=a_2, where a_1, a_2 a are constants, the system is a generalized diffusion model equation in population problem. 相似文献
11.
一类二阶具偏差变元的微分方程周期解 总被引:29,自引:0,他引:29
本文利用重合度理论研究一类二阶具偏差变元的微分方程x''(t)+f(t,x(t),x(t-τ0(t)))x'(t)+β(t)g(x(t-τ1(t)))=p(t)的周期解问题,得到了存在周期解的新的结果. 相似文献
12.
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
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
13.
一类二阶迭代微分方程的周期解 总被引:8,自引:0,他引:8
利用拓扑度理论研究了一类二阶迭代泛函微分方程x(t) g(x(x(t)))=f(t,x(t),x(t))的周期解的存在性,得出了周期解存在的充分条件. 相似文献
14.
一类二阶n-维中立型微分系统周期解问题 总被引:8,自引:0,他引:8
笔者利用重合度原理研究一类二阶n-维中立型微分系统(d2)/(dt2)(x(t)-Cx(t- ))+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果,推广了已有工作中相应的结论. 相似文献
15.
On existence of positive periodic solutions of a kind of Rayleigh equation with a deviating argument
The existence of positive periodic solutions for a kind of Rayleigh equation with a deviating argument
$
x'(t) + f(x'(t)) + g(t,x(t - \tau (t))) = p(t)
$
x'(t) + f(x'(t)) + g(t,x(t - \tau (t))) = p(t)
相似文献
16.
17.
利用重合度理论和不等式分析技巧,获得了一类具有偏差变元的高阶中立型Rayleigh方程(x(t)-cx(t-σ))~((m))+f(x'(t))+β(t)g(x(t-τ(t)))=p(t)周期解存在性的新的充分条件,有意义的是函数f(x)和非线性项前的系数β(t)可以变号. 相似文献
18.
本文利用重合度理论和 V-泛函研究了一类具有周期输入的广义时滞 Hopfield型连续神经网络系统的平稳周期振荡问题 ,得到了其周期解存在、唯一和全局吸引的充分条件 . 相似文献
19.
该文利用一个严格集压缩不动点定理,得到了如下形式的一类时标上具状态依赖时滞的中立型泛函微分方程周期正解存在性的充分条件x~Δ(t)=x(t)[r(t)-a(t)x(t)-sum from j=1 to n a_j(t)x(t-Υ_j(t,x(t)))-sum from j=1 to n c_j(t)x~Δ(t-σ_j(t,x(t)))],其中r,a,a_j,c_j∈C(T,R~+)(j=1,2,…,n)是ω-周期函数,Υ_j,σ_j∈C(T×R,T)(j=1,2,…,n)分别是其第一变元的ω-周期函数. 相似文献
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