共查询到20条相似文献,搜索用时 0 毫秒
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讨论解的存在区间,说明周期函数如何是周期解以及它和Poincaré映射的关系.对周期的Riccati方程研究了周期解的个数,是文[8]中的定理1的一个补充,同时也研究了周期捕获的人口方程解的存在区间和周期解问题. 相似文献
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本文考虑非线性常微分方程组周期解的存在性,得到了周期解的Nagumo型先验估计,由此在一般性条件下证明了方程组至少有一个T-周期解, 相似文献
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Zhaoli Liu 《数学学报(英文版)》2000,16(3):505-514
Abstract
This paper is concerned with the existence of periodic solutions for a nonlinear system of ordinary differential equations.
We obtain a Nagumo-type a priori bound for the periodic solutions and then by using this a priori bound we prove the existence of at least one T-periodic solution under some general conditions
Research supported by the NNSF of China and the RFDP of China. 相似文献
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二阶非线性常微分方程的正周期解 总被引:29,自引:0,他引:29
本文应用Krasnoselskii锥映射不动点定理,研究了二阶非线性常微分方程的ω-周期解的存在性,获得了若干正ω-周期解的存在性与多重性结果. 相似文献
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非线性二阶常微分方程的正周期解 总被引:2,自引:0,他引:2
讨论一类非线性二阶常微分方程的周期解问题 ,利用Banach空间锥上的不动点定理得到了正周期解的存在性和多重性结果 ,大大改进了文献 [1 ]的结果 相似文献
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Yong Xiang LI 《数学学报(英文版)》2005,21(3):491-496
In this paper the existence results of oscillatory periodic solutions are obtained for a second order ordinary differential equation -u″(t) = f(t, u(t)), where f : R^2 → R is a continuous odd function and is 2π-periodic in t. The discussion is based on the fixed point index theory in cones. 相似文献
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本文运用了比较新的手法,证明了非线性微分系统(dx)/(dt)=1/(a(x))[c(y)-b(x)];(dy)/(dt)=-a(x)[h(x)-e(t)](1)(其中a(x),b(x),h(x),c(y),e(t)为连续可微函数,x,y∈R,t∈[0,+∞),且a(x)>0)解的有界性及周期解的存在性,并应用该结论讨论了强迫振动方程:x+(f(x)+g(x)x)x+h(x)=e(t)(2)(其中f(x),g(x)为连续可微函数,x∈R,h(x),e(t)同上)解的有界性及周期解的存在性. 相似文献
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We establish the existence, multiplicity and nonexistence of positive periodic solutions of systems of second order ordinary
differential equations. 相似文献
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Consider the n-dimensional nonautonomous system ?(t) = A(t)G(x(t)) ? B(t)F(x(t ? τ(t))) Let u = (u 1,…,u n ), $f^{i}_{0}={\rm lim}_{\|{\rm u}\|\rightarrow 0}{f^{i}(\rm u)\over \|u\|}$ , $f^{i}_{\infty}={\rm lim}_{\|{\rm u}\|\rightarrow \infty}{f^{i}(\rm u)\over \|u\|}$ , i = l,…,n, F = (f 1…,f n ), ${\rm F_{0}}={\rm max}_{i=1,\ldots,n}{f^{i}_{0}}$ and ${\rm F_{\infty}}={\rm max}_{i=1,\ldots,n}{f^{i}_{\infty}}$ . Under some quite general conditions, we prove that either F0 = 0 and F∞ = ∞, or F0 = ∞ and F∞ = 0, guarantee the existence of positive periodic solutions for the system for all λ > 0. Furthermore, we show that F0 = F∞ = 0, or F∞ = F∞ = ∞ guarantee the multiplicity of positive periodic solutions for the system for sufficiently large, or small λ, respectively. We also establish the nonexistence of the system when either F0 and F∞ > 0, or F0 and F∞, < for sufficiently large, or small λ, respectively. We shall use fixed point theorems in a cone. 相似文献
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Cong Fuzhong 《东北数学》1997,(2)
PeriodicSolutionsforNonlinearDiferentialEquationsCongFuzhong(从福仲)(OfficeofMathematics,86003Unit,Changchun,130022)MaoDongming(... 相似文献
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A. K. Demenchuk 《Ukrainian Mathematical Journal》2005,57(8):1325-1333
For weakly nonlinear almost periodic ordinary differential systems, we obtain conditions for the existence of partially irregular
almost periodic solutions and propose algorithms for their construction.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1123 – 1130, August, 2005. 相似文献
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This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form 相似文献