共查询到18条相似文献,搜索用时 78 毫秒
1.
This paper studies the variation of constant formulae for linear Caputo fractional delay differential systems. We discuss the exponential estimates of the solutions for linear time invariant fractional delay differential systems by using the Gronwall's integral inequality. The variation of constant formula for linear time invariant fractional delay differential systems is obtained by using the Laplace transform method. In terms of the superposition principle of linear systems and fundamental solution matrix, we also establish the variation of constant formula for linear time varying fractional delay differential systems. The obtained results generalize the corresponding ones of integer-order delayed differential equations. 相似文献
2.
Zhou Zhengxin Zhang Shanlin 《Annals of Differential Equations》2005,21(3):529-532
Using reflecting function of Mironenko we construct some nonautonomous differential systems which are equivalent to the given autonomous differential systems. The results are applied to discuss the existence and stability of periodic solution of these nonautonomous nonlinear differential systems. 相似文献
3.
高凌云 《数学物理学报(B辑英文版)》2010,30(3):932-938
We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations. 相似文献
4.
《Annals of Differential Equations》2008,(1):100-104
In this paper,the all-delay stability of degenerate differential systems with delay is discussed.We come up with some new criteria for evaluating the all-delay stability of degenerate differential systems with delay and degenerate neutral differential systems with delay.Also,we give an example to illustrate the main results. 相似文献
5.
高凌云 《数学物理学报(B辑英文版)》2010,(5):1507-1513
In this article, we mainly investigate the behavior of systems of complex differential equations when we add some condition to the quality of the solutions, and obtain an interesting result, which extends Gaekstatter and Laine's result concerning complex differential equations to the systems of algebraic differential equations. 相似文献
6.
Applying the Nevanlinna theory of meromorphic function,we investigate the non-admissible meromorphic solutions of nonlinear complex algebraic differential equation and gain a general result.Meanwhile,we prove that the meromorphic solutions of some types of the systems of nonlinear complex differential equations are non-admissible.Moreover,the form of the systems of equations with admissible solutions is discussed. 相似文献
7.
On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations 总被引:3,自引:0,他引:3
Ling-yun Gao 《应用数学学报(英文版)》2005,21(3):499-504
This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda's results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations. 相似文献
8.
Lynn ERBE Christopher C. TISDELL Patricia J. Y. WONG 《数学学报(英文版)》2007,23(3):549-556
Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions. 相似文献
9.
We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class of rational differential systems with a cubic polynomial as its numerator. 相似文献
10.
微分系统的反射函数与周期解 总被引:1,自引:0,他引:1
周正新 《高校应用数学学报(英文版)》2002,17(1):13-23
This article deals with the reflective function of the mth-order nonlinear differential systems. The results are applied to discussing the stability property of periodic solutions of these systems. 相似文献
11.
本文讨论非线性退化时滞微分控制系统.首先就非线性退化时滞微分控制系统的一阶变分系统给出变易公式,然后就非线性退化时滞微分控制系统的一阶变分系统的函数能控性给出一些判据,最后给出关于非线性退化时滞微分控制系统的函数能控性的判据. 相似文献
12.
On the equivalence of two differential equations by means of reflecting functions coinciding 下载免费PDF全文
In this article, we discuss the equivalence of two differential systems by using the method of reflecting functions. We obtain some necessary and sufficient conditions under which certain differential equations are equivalent. Given these results, new types of differential systems equivalent to the given systems can be found. We also discussed the qualitative behavior of the periodic solutions of such differential systems. These results are new, in the sense that they generalize previous discussions on the equivalence of differential systems. 相似文献
13.
THE V-FUNCTIONAL METHOD FOR THE STABILITY OF DEGENERATE DIFFERENTIAL SYSTEMS WITH DELAYS 总被引:3,自引:0,他引:3
1 IntroductionStability is an important perfermance index of concrete systems such asmanagement systems, power systems, engineering systems and so on. Forthe stability V--functional criterion method of functional differential systems,have had many results in recent years, see) for example, [1] and [2]. Andfor degenerate systems, papers [41-[81 have carefully discussed and given someimportant results. But we note that (see [9]) many concrete systems, besidescontain delay, are degenerate. So, f… 相似文献
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15.
P. H. Anh Ngoc S. Murakami T. Naito J. Son Shin Y. Nagabuchi 《Integral Equations and Operator Theory》2009,64(3):325-355
We first introduce the notion of positive linear Volterra-Stieltjes differential systems. Then, we give some characterizations
of positive systems. An explicit criterion and a Perron-Frobenius type theorem for positive linear Volterra-Stieltjes differential
systems are given. Next, we offer a new criterion for uniformly asymptotic stability of positive systems. Finally, we study
stability radii of positive linear Volterra-Stieltjes differential systems. It is proved that complex, real and positive stability
radius of positive linear Volterra-Stieltjes differential systems under structured perturbations coincide and can be computed
by an explicit formula. The obtained results in this paper include ones established recently for positive linear Volterra
integro-differential systems [36] and for positive linear functional differential systems [32]-[35] as particular cases. Moreover,
to the best of our knowledge, most of them are new.
The first author is supported by the Alexander von Humboldt Foundation. 相似文献
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17.
G. V. Demidenko V. A. Likhoshvai T. V. Kotova Yu. E. Khropova 《Siberian Mathematical Journal》2006,47(1):45-54
We establish a connection between solutions to a broad class of large systems of ordinary differential equations and solutions to retarded differential equations. We prove that solving the Cauchy problem for systems of ordinary differential equations reduces to solving the initial value problem for a retarded differential equation as the number of equations increases unboundedly. In particular, the class of systems under consideration contains a system of differential equations which arises in modeling of multiphase synthesis. 相似文献
18.
A. A. Bolibrukh 《Proceedings of the Steklov Institute of Mathematics》2011,272(2):13-43
The following problems of the analytic theory of differential equations are considered: Hilbert’s 21st problem for Fuchsian systems of linear differential equations, the Birkhoff normal form problem for systems of linear differential equations with irregular singularities, and the classification problem for isomonodromic deformations of Fuchsian systems. 相似文献