共查询到20条相似文献,搜索用时 15 毫秒
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By using the roughness theory of exponential dichotomies and the contraction mapping, some sufficient conditions are obtained for the existence and uniqueness of pseudo almost periodic solution of the above differential equation with piecewise constant argument
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Rong Yuan 《中国科学A辑(英文版)》1998,41(3):232-241
By constructing almost periodic sequence solutions to difference equations, the existence of almost periodic solutions of
neutral delay differential equations with piecewise constant argument
is studied.
Project supported by the National Natural Science Foundation of China. 相似文献
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R. Yuan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1999,23(3):94-119
Based on the investigation of almost periodic solutions to difference equations, the existence of almost periodic solution for a nonautonomous, singularly perturbed differential equation with piecewise constant argument is considered. In addition, the stability properties of these solutions are characterized by the construction of manifolds of initial data. 相似文献
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YUAN Rong 《中国科学A辑(英文版)》2000,43(4):371-383
A definition of pseudo almost periodic sequence is given and the existence of pseudo almost periodic sequence to difference
equation is studied. Based on these, the existence of pseudo almost periodic solutions to neutral delay differential equations
with piecewise constant argument is investigated 相似文献
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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
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PIAO Daxiong 《中国科学A辑(英文版)》2001,44(9)
In this paper, we investigate the existence and uniqueness of new almost periodic type solutions, so-called pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument by means of introducing the notion of pseudo almost periodic vector sequences. 相似文献
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Rong Yuan 《Journal of Mathematical Analysis and Applications》2005,303(1):103-118
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
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In this paper, the spectrum relation of almost periodic solution for the equation (x(t) + px(t − 1))″ = qx([t]) + f(t) is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some
part of the spectrum inclusion in that article is not correct. The key point which causes such problem is found out. A new
statement is formulated and proved. 相似文献
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On the existence of almost periodic solutions of some dissipative second order differential equations 总被引:1,自引:0,他引:1
J. O. C. Ezeilo 《Annali di Matematica Pura ed Applicata》1964,65(1):389-405
Summary The search for almost periodic solutions of any dissipative equation of the form(1.1), in which p(t) is an almost periodic function, has come to be closely linked up with a number of standard ? convergence ?
restrictions on f, g′, g″ and k (see, for example,[2] and[3]). The object of the present paper is to show that as far as the existence, alone, of an almost periodic solution of(1.1) is concerned these ? convergence ? restrictions on f, g′, g″ and k are quite unnecessary. The first result (Theorem 1) shows
in fact that the conditions(1.2) alone are quite sufficient for the existence of an almost periodic solution of(1.1); and Theorem 2 extends this result (though under stronger conditions on f and g) to the case in which the forcing function
depends on x and x as well.
Partially supported by N.S.F. research project G-57 at The University of Michigan. 相似文献
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《Applied Mathematics Letters》2000,13(2):131-137
The existence of almost periodic, asymptotically almost periodic, and pseudo almost periodic solutions of differential equations with piecewise constant argument is characterized in terms of almost periodic, asymptotically, and pseudo almost periodic sequences. Thus Meisters's and Opial's theorems are extended. 相似文献
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通过构造差分方程的渐近概周期序列解,研究了三阶中立型逐段常变量微分方程渐近概周期解的存在性. 相似文献
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Daxiong Piao 《中国科学 数学(英文版)》2001,44(9):1156-1161
In this paper, we investigate the existence and uniqueness of new almost periodic type solutions, so-called pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument by means of introducing the notion of pseudo almost periodic vector sequences 相似文献
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By means of Mawhin's continuation theorem, we study some second order differential equations with a deviating argument:
x″(t)=f(t,x(t),x(t−τ(t)),x′(t))+e(t). 相似文献
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Existence of almost periodic solutions for forced perturbed systems with piecewise constant argument
Certain almost periodic forced perturbed systems with piecewise argument are considered in this paper. By using the contraction mapping principle and some new analysis technique, some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution of these systems. Furthermore, we study the harmonic and subharmonic solutions of these systems. The obtained results generalize the previous known results such as [A.M. Fink, Almost Periodic Differential Equation, Lecture Notes in Math., vol. 377, Springer-Verlag, Berlin, 1974; C.Y. He, Almost Periodic Differential Equations, Higher Education Press, Beijing, 1992 (in Chinese); Z.S. Lin, The existence of almost periodic solution of linear system, Acta Math. Sinica 22 (5) (1979) 515-528 (in Chinese); C.Y. He, Existence of almost periodic solutions of perturbation systems, Ann. Differential Equations 9 (2) (1992) 173-181; Y.H. Xia, M. Lin, J. Cao, The existence of almost periodic solutions of certain perturbation system, J. Math. Anal. Appl. 310 (1) (2005) 81-96]. Finally, a tangible example and its numeric simulations show the feasibility of our results, the comparison between non-perturbed system and perturbed system, the relation between systems with and without piecewise argument. 相似文献
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In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equations. 相似文献
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In this paper, we investigate qualitative behavior of nonlinear differential equations with piecewise constant argument (PCA). A topological approach of Wa?ewski-type which gives sufficient conditions to guarantee that the graph of at least one solution stays in a given domain is formulated. Moreover, our results are also suitable for a class of general system of discrete equations. By using a regular polyfacial set, we apply our developed topological approach to cellular neural networks (CNNs) with PCA. Some new results are attained to reveal dynamic behavior of CNNs with PCA and discrete-time CNNs. Finally, an illustrative example of CNNs with PCA shows usefulness and effectiveness of our results. 相似文献