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1.
We study the spectrum containment of almost periodic solution to second order differential equations with piecewise constant argument. Some known (periodic, quasi-periodic) results would be expanded. As a corollary, it is shown that such equations with periodic perturbations possess a quasi-periodic solution and no periodic solution. This phenomena is due to the piecewise constant argument. The results are extended to nonlinear equations.  相似文献   

2.
In the first part of this paper, we obtain a new property on the module containment for almost periodic functions. Based on it, we establish the module containment of an almost periodic solution for a class of differential equations with piecewise constant delays. In the second part, we investigate the existence, uniqueness and exponential stability of a positive almost periodic and quasi-periodic solution for a certain class of logistic differential equations with a piecewise constant delay. The module containment for the almost periodic solution is established.  相似文献   

3.
We study the spectrum containment of almost periodic solution to neutral delay differential equations with piecewise constant argument (EPCA, for short). We find an important property, which is different from that given by Cartwright for ordinary differential equations (ODE). Some known (periodic solution) results would be expanded. As a corollary, it is shown that EPCA with periodic perturbations possess a quasi-periodic solution and no periodic solution. This new phenomenon is due to the piecewise constant argument and illustrates a crucial difference between ODE and EPCA.  相似文献   

4.
In this paper we continue to consider differential equations with piecewise constant argument of generalized type (EPCAG) [M.U. Akhmet, Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. TMA 66 (2007) 367–383]. A deviating function of a new form is introduced. The linear and quasilinear systems are under discussion. The structure of the sets of solutions is specified. Necessary and sufficient conditions for stability of the zero solution are obtained. Our approach can be fruitfully applied to the investigation of stability, oscillations, controllability and many other problems of EPCAG. Some of the results were announced at The International Conference on Hybrid Systems and Applications, University of Louisiana, Lafayette, 2006.  相似文献   

5.
利用Halanay不等式,我们得到了一类具有逐段常变量神经网络系统解全局指数稳定的一个充分条件;此外,在同样条件下,通过不动点定理,证明了这类概周期系统概周期解的存在唯一性与模包含关系.  相似文献   

6.
This paper is concentrated on giving a module containment theorem for piecewise continuous almost periodic functions (pcap function for short). One first analyses the relationship between the translation number set and some Fourier exponents of a pcap function. And then, combining with Kronecker’s theorem, a module containment theorem for a pcap function is established for the first time. As an application, the module structure of a pcap solution for an impulsive differential equation is characterized. Some remarks and a corollary are given to show the advantage of the module containment theorem.  相似文献   

7.
A new class of differential equations with state-dependent piecewise constant argument is introduced. It is an extension of systems with piecewise constant argument. Fundamental theoretical results for the equations—the existence and uniqueness of solutions, the existence of periodic solutions, and the stability of the zero solution—are obtained. Appropriate examples are constructed.  相似文献   

8.
Oscillatory, nonoscillatory, and periodic solutions of re-tarded functional differential equations are investigated. The study concerns a system of two first order linear equations with piecewise constant argument.  相似文献   

9.
Oscillatory properties of retarded and advanced functional differential equations are investigated.In the first part, the study concerns equations with piecewise constant arguments, which found applications in certain biomedical problems. Then, results of some authors are generalized for general equations with many argument deviations. Finally, applications are given to equations with linear transformations of the argument.  相似文献   

10.
51.Intr0ducti0nInthispaper,weconsidertheexistenceofalmostperiodicsoluti0nsforthefoll0wingneutralfunctionaldifferentialebuationwithpiecewiseconstantargument:wherep,qarenonzeroconstants,p(t)lsanalmostper1odicfunctlon,g:RXRXR-Risanalm0stperiodicfunctionintanduniformlyonRXR,andL.jstandsforthegreatest-integerfunction.Notethatforanyintegern,if2n-10)andtheequations(1),(2)areadvanced(orretardedrespectively).Differentialequationswithpiecewiseconstantar…  相似文献   

11.
We obtain sufficient conditions for the existence of almost periodic solutions of almost periodic linear differential equations thereby extending Favard's classical theorem. These results are meant to complement previous results of the authors who have shown by means of a counterexample that the boundedness of all solutions is not, by itself, sufficient to guarantee the existence of an almost periodic solution to a linear almost periodic differential equation.

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12.
In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.  相似文献   

13.
The well-known Favard's theorem states that the linear differential equation
(1)  相似文献   

14.
A general module containment property is proved for almost periodic linear systems of differential equations, in both finite and infinite dimensions.  相似文献   

15.
We study the existence of quasi-periodic solutions to differential equations with piecewise constant argument (EPCA, for short). It is shown that EPCA with periodic perturbations possess a quasi-periodic solution and no periodic solution. The appearance of quasi-periodic rather than periodic solutions is due to the piecewise constant argument. This new phenomenon illustrates a crucial difference between ODE and EPCA. The results are extended to nonlinear equations.  相似文献   

16.
We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument.  相似文献   

17.
Using spectral theory we obtain sufficient conditions for the almost automorphy of bounded solutions to differential equations with piecewise constant argument of the form x(t)=A(t)x([t])+f(t),tR, where A(t) is an almost automorphy operator, f(t) is an X-valued almost automorphic function and X is a finite dimensional Banach space.  相似文献   

18.
We study scalar advanced and delayed differential equations with piecewise constant generalized arguments, in short DEPCAG of mixed type, that is, the arguments are general step functions. It is shown that the argument deviation generates, under certain conditions, oscillations of the solutions, which is an impossible phenomenon for the corresponding equation without the argument deviations. Criteria for existence of periodic solutions of such equations are discussed. New criteria extend and improve related results reported in the literature. The efficiency of our criteria is illustrated via several numerical examples and simulations.  相似文献   

19.
We study the existence of oscillatory and periodic solutions of a class of first order scalar impulsive delay differential equations with piecewise constant argument.  相似文献   

20.
This paper continues the investigation of differential equations with piecewise constant argument using differential inequalities. The monotone method is used to prove the existence of minimal and maximal solutions for the delay differential equations of the form x′(t) = f(t, x(t), x([t])), x(0) = C0.  相似文献   

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