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1.
N. B. Zhuravlev 《Journal of Mathematical Sciences》2008,153(5):683-709
In this paper, a hyperbolicity criterion for periodic solutions of nonlinear functional-differential equations is constructed
in terms of zeros of the characteristic function. In the earlier papers in this area, necessary and sufficient conditions
were different from each other. Moreover, it was assumed that if the period of the investigated solution is irrational, then
that solution admits a rational approximation. In this paper, we obtain necessary and sufficient conditions of the hyperbolicity.
It is proved (and the proof is constructive) that a rational approximation exists for any irrational period. All the results
are obtained for the case of several rational delays.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 21, Proceedings of the Seminar on Differential and Functional Differential Equations Supervised by A. Skubachevskii (Peoples’
Friendship University of Russia), 2007. 相似文献
2.
《Nonlinear Analysis: Real World Applications》2008,9(5):2214-2221
By using a fixed point theorem of strict-set-contraction, some criteria are established for the existence of positive periodic solutions of neutral functional differential equations with distributed delays and feedback control. 相似文献
3.
Jean Mawhin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1987,38(2):257-265
The method of upper and lower solutions and convexity arguments are used to prove sharp results for the existence and multiplicity of periodic solutions for first order ordinary differential equations depending upon a parameter.Dedicated to Professor H. W. Knobloch for his sixtieth birthday 相似文献
4.
《Journal of Computational and Applied Mathematics》2005,174(2):201-211
In this paper, we study stability of periodic solutions of a class of nonlinear functional differential equations (FDEs) with state-dependent delays using the method of linearization. We show that a periodic solution of the nonlinear FDE is exponentially stable, if the zero solution of an associated linear periodic linear homogeneous FDE is exponentially stable. 相似文献
5.
Positive periodic solutions of functional differential equations 总被引:1,自引:0,他引:1
Haiyan Wang 《Journal of Differential Equations》2004,202(2):354-366
We consider the existence, multiplicity and nonexistence of positive ω-periodic solutions for the periodic equation x′(t)=a(t)g(x)x(t)−λb(t)f(x(t−τ(t))), where are ω-periodic, , , f,g∈C([0,∞),[0,∞)), and f(u)>0 for u>0, g(x) is bounded, τ(t) is a continuous ω-periodic function. Define , , i0=number of zeros in the set and i∞=number of infinities in the set . We show that the equation has i0 or i∞ positive ω-periodic solution(s) for sufficiently large or small λ>0, respectively. 相似文献
6.
John Mallet-Paret 《Journal of Differential Equations》1977,25(2):163-183
Consider the class of retarded functional differential equations , (1) where xt(θ) = x(t + θ), ?1 ? θ ? 0, so xt?C = C([?1, 0], Rn), and . Let 2 ? r ? ∞ and give the appropriate (Whitney) topology. Then the set of such that all fixed points and all periodic solutions of (1) are hyperbolic is residual in . 相似文献
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8.
We study a nonlinear neutral functional differential equation. Applying the properties of almost periodic function and exponential dichotomy of linear system as well as Krasnoselskii’s fixed point theorem, we establish the conditions for the existence of almost periodic solution of the equations. 相似文献
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10.
We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results. 相似文献
11.
We consider a class of scalar linear differential equations with several variable delays and constant coefficients. A family of equations of the class is defined by coefficients and maximum admissible values of delays. We obtain conditions that are necessary and sufficient for the stability of solutions to all equations of the family. It is ascertained that the conditions are determined entirely by properties of the solution to the initial problem for an autonomous equation that belongs to the family. Some alternatives of required conditions are obtained in the form of estimates for solutions to autonomous equations in a finite interval. 相似文献
12.
We prove the existence and multiplicity of positive T-periodic solution(s) for T-periodic equation x′(t)=h(t,x)−λb(t)f(x(t−τ(t))) by Krasnoselskii fixed point theorem, where f(x) may be singular at x=0. Our results improve some recent results in previous literature. 相似文献
13.
赵晓强 《应用数学学报(英文版)》1993,9(4):328-334
In this paper,using Mawhin's continuation theorem in the theory of coincidence degree,we first prove the general existence theorem of periodic solutions for F.D.Es with infinite delay:dx(t)/dt=f(t,x_t),x(t)∈R~n,which is an extension of Mawhin's existence theorem of periodic solutions of F.D.Es with finite delay.Second,as an application of it,we obtain the existence theorem of positive periodic solutions of the Lotka-Volterra equations:dx(t)/dt=x(t)(a-kx(t)-by(t)),dy(t)/dt=-cy(t)+d integral from n=0 to +∞ x(t-s)y(t-s)dμ(s)+p(t). 相似文献
14.
We consider a class of scalar linear differential equations with several variable delays and constant coefficients. We treat the coefficients and maximum admissible values of delays as parameters that define a family of equations of the considered class. Using the necessary and sufficient stability conditions established in preceding papers, we obtain an analytic form and a geometric interpretation of boundaries of stability domains for families of equations with a small number of independent parameters. 相似文献
15.
We consider a class of scalar linear differential equations with several variable delays and constant coefficients. We treat coefficients and maximum admissible values of delays as parameters that define a family of equations from the class under consideration. We study domains in the parameter space, where fundamental solutions of all equations of the family are uniformly or exponentially stable and have a fixed sign. We establish explicit necessary and sufficient conditions for the stability and sign-definiteness of the equations family. 相似文献
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《Nonlinear Analysis: Real World Applications》2008,9(3):977-984
In this paper, a type of nonlinear neutral functional differential equations are considered. Some results on the existence of three positive periodic solutions are obtained by using the Leggett–Williams fixed point theorem. 相似文献
19.
In this paper, we investigate a class of stochastic functional differential equations of the form
dx(t)=(Ax(t)+F(t,x(t),xt))dt+G(t,x(t),xt)°dW(t). 相似文献
20.
In this paper, we consider a type of second-order neutral functional differential equations. We obtain some existence results of multiplicity and nonexistence of positive periodic solutions. Our approach is based on a fixed point theorem in cones. 相似文献