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ASYMPTOTIC EQUIVALENCE OF ALTERNATELY ADVANCED AND DELAYED DIFFERENTIAL SYSTEMS WITH PIECEWISE CONSTANT GENERALIZED ARGUMENTS 被引量:1
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作者 Kuo-Shou CHIU 《Acta Mathematica Scientia》 SCIE CSCD 2018年第1期220-236,共17页
In this paper, we investigate the existence, uniqueness and the asymptotic equiv- alence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of... In this paper, we investigate the existence, uniqueness and the asymptotic equiv- alence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of generalized type (DEPCAG). This is based in the study of an equivalent integral equation with Cauchy and Green matrices type and in a solution of a DEPCAG integral inequality of Gronwall type. Several examples are also given to show the feasibility of results. 展开更多
关键词 piecewise constant argument of generalized type hybrid equations EQUIVALENCE asymptotic behavior Gronwall's inequality
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Asymptotically Antiperiodic Solutions for a Nonlinear Differential Equation with Piecewise Constant Argument in a Banach Space
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作者 William Dimbour Vincent Valmorin 《Applied Mathematics》 2016年第15期1726-1733,共8页
In this paper, we give sufficient conditions for the existence and uniqueness of asymptotically w-antiperiodic solutions for a nonlinear differential equation with piecewise constant argument in a Banach space when w ... In this paper, we give sufficient conditions for the existence and uniqueness of asymptotically w-antiperiodic solutions for a nonlinear differential equation with piecewise constant argument in a Banach space when w is an integer. This is done using the Banach fixed point theorem. An example involving the heat operator is discussed as an illustration of the theory. 展开更多
关键词 Asymptotically ω-Antiperiodic Functions differential equations with piecewise constant Argument Semi-Group
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Analytical Approach to Differential Equations with Piecewise Continuous Arguments via Modified Piecewise Variational Iteration Method
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作者 Qi Wang 《Journal of Applied Mathematics and Physics》 2014年第1期26-31,共6页
In the present article, we apply the modified piecewise variational iteration method to obtain the approximate analytical solutions of the differential equations with piecewise continuous arguments. This technique pro... In the present article, we apply the modified piecewise variational iteration method to obtain the approximate analytical solutions of the differential equations with piecewise continuous arguments. This technique provides a sequence of functions which converges to the exact solution of the problem. Moreover, this method reduces the volume of calculations because it does not need discretization of the variables, linearization or small perturbations. The results seem to show that the method is very reliable and convenient for solving such equations. 展开更多
关键词 Delay differential equationS piecewise CONTINUOUS arguments VARIATIONAL ITERATION Method Approximation
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THE CONVERGENCE OF TRUNCATED EULER-MARUYAMA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH PIECEWISE CONTINUOUS ARGUMENTS UNDER GENERALIZED ONE-SIDED LIPSCHITZ CONDITION
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作者 Yidan Geng Minghui Song Mingzhu Liu 《Journal of Computational Mathematics》 SCIE CSCD 2023年第4期663-682,共20页
In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coef... In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory. 展开更多
关键词 Stochastic differential equations piecewise continuous argument One-sided Lipschitz condition Truncated Euler-Maruyama method
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Global Stability in a Differential Equation with Piecewisely Constant Arguments 被引量:1
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作者 刘玉记 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2001年第1期31-36,共6页
In this paper we consider the differential equation with piecewisely constant arguments where ['] -denotes the greates integer function, r(t) E C([0,+∞),(0, +∞)),Pi ∈ [0, +∞)(i = 1, 2,''' , m), wit... In this paper we consider the differential equation with piecewisely constant arguments where ['] -denotes the greates integer function, r(t) E C([0,+∞),(0, +∞)),Pi ∈ [0, +∞)(i = 1, 2,''' , m), with Pm > 0, we establish some new sufficient conditions for an arbitrary solution N(t) to satisfy the initial conditions of the form N(0) = NO > 0 and N(-j) = N-j ≥ 0,j = 1, 2, ., m, to converge to the positive equilibrium N* as t →∞. 展开更多
关键词 differential equation global stability piecewise constant argument.
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Almost Periodic Solutioiis of Neutral Differential Difference Equations with Piecewise Constant Arguments 被引量:3
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作者 PIAO Da Xiong Department of Mathematics,Fushun Petroleum Institute.Fushun 113001,P.R.China E-mail:piaodx@fspu.edu.cn 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2002年第2期263-276,共14页
In this paper,we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.
关键词 Almost periodic functions Almost periodic sequences piecewise constant arguments Neutral differential difference equations
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Weighted Pseudo Almost Periodic Solutions of N-th Order Neutral Differential Equations with Piecewise Constant Arguments 被引量:3
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作者 Rong Kun ZHUANG Rong YUAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第7期1259-1272,共14页
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 ... 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. 展开更多
关键词 Weighted pseudo almost periodic sequence weighted pseudo almost periodic solution neutral differential equation piecewise constant arguments
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OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF FIRST ORDER DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DEVIATING ARGUMENTS 被引量:4
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作者 冯月才 戴运恩 《Annals of Differential Equations》 1999年第4期345-351,共7页
In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for osc... In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for oscillatory and asymptoticbehavior of solutions of the equation. 展开更多
关键词 piecewise constant deviating arguments neutral differential equa-tion OSCILLATORY BEHAVIOR asymptotic BEHAVIOR
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NONLINEAR BOUNDARY VALUE PROBLEMS FOR FIRST ORDER DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS 被引量:1
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作者 张凤琴 马知恩 《Annals of Differential Equations》 2003年第3期431-438,共8页
The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equatio... The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equations with piecewise constant arguments. 展开更多
关键词 nonlinear boundary value problem monotone iterative technique lower and upper related solutions differential equations with piecewise constant arguments
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STABILITY IN DIFFERENTIAL EQUATIONS WITH CONTINUOUS AND PIECEWISE CONSTANT ARGUMENTS 被引量:1
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作者 Ming-Po Chen 《Annals of Differential Equations》 1996年第4期387-391,共5页
Consider the delay differential equation with continuous and piecewise constant argumentswhere [·] denotes the greatest integer function. We obtain sufficient conditions for thezero solution of (1) to be (asympt... Consider the delay differential equation with continuous and piecewise constant argumentswhere [·] denotes the greatest integer function. We obtain sufficient conditions for thezero solution of (1) to be (asymptotically) stable.1991 Mathematics Subject Classification: 39A12. 展开更多
关键词 equations with continuous and piecewise constant arguments STABILITY
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LINEARIZED OSCILLATIONS OF DELAY DIFFERENTIAL EQUATIONS AND APPLICATIONS
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作者 WANGYOUBIN ZHAOAIMIN YANJURANG 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1998年第4期391-396,共6页
The necessary and sufficient conditions for the oscillations of every solution of the nonlinear delay equation (t)+f(x(t-l))+g(x( t-k ))=0 are oblained.
关键词 OSCILLATION nonlinear delay equation continuous and piecewise constant argument
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Existence of almost periodic solutions of neutral differential equations with piecewise constant argument 被引量:18
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作者 袁荣 洪佳林 《Science China Mathematics》 SCIE 1996年第11期1164-1177,共14页
Based on the properties on almost periodic sequence, it is proved that the almost periodic solutions for a class of neutral differential equations with piecewise constant argument exist.
关键词 ALMOST PERIODIC solutions ALMOST PERIODIC sequences piecewise constant ARGUMENT neutral differential equations.
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The Existence of Pseudo-almost Periodic Solutions of Third-order Neutral Differential Equations with Piecewise Constant Argument 被引量:5
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作者 Rong Kun ZHUANG Rong YUAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第5期943-958,共16页
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 equ... 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. 展开更多
关键词 Pseudo-almost periodic solutions pseudo-almost periodic sequences neutral delay equation piecewise constant argument
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A Spectrum Relation of Almost Periodic Solution of Second Order Scalar Functional Differential Equations with Piecewise Constant Argument 被引量:4
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作者 Li WANG Rong YUAN Chuan Yi ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第11期2275-2284,共10页
In this paper, the spectrum relation of almost periodic solution for the equation (x(t) +px(t - 1))" = qx([t]) + f(Q is investigated. Although this has been discussed in an article, some counterexamples ar... In this paper, the spectrum relation of almost periodic solution for the equation (x(t) +px(t - 1))" = qx([t]) + f(Q 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. 展开更多
关键词 Neutral delay-differential equation piecewise constant argument almost periodicity SPECTRUM
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Existence of almost periodic solutions of second order neutral delay differential equations with piecewise constant argument 被引量:9
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作者 袁荣 《Science China Mathematics》 SCIE 1998年第3期232-241,共10页
By constructing almost periodic sequence solutions to difference equations, the existence of almost periodic solutions of neutral delay differential equations with piecewise constant argument $$\frac{{d^2 }}{{dt^2 }}(... By constructing almost periodic sequence solutions to difference equations, the existence of almost periodic solutions of neutral delay differential equations with piecewise constant argument $$\frac{{d^2 }}{{dt^2 }}(x(t) + px(t - 1)) = qr\left( {2\left[ {\frac{{t + 1}}{2}} \right]} \right) + g{\bf{ }}(t,x(t),x([t]))$$ is studied. 展开更多
关键词 ALMOST PERIODIC solutions ALMOST PERIODIC sequences neutral delay equation piecewise constant argu-ment.
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A New Almost Periodic Type Solution of First Order Neutral Delay Differential Equations with Piecewise Constant Argument 被引量:2
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作者 Rong YUAN Department of Mathematics,Beijing Normal University,Beijing 100875,P.R.China E-mail:ryuan@bnu.edu.cn 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2001年第3期403-412,共10页
In this paper,we introduce a new class of ergodic sequences,pseudo almost periodic sequences,and study the existence of pseudo almost periodic sequences to difference equations.On the basis of these,we investigate the... In this paper,we introduce a new class of ergodic sequences,pseudo almost periodic sequences,and study the existence of pseudo almost periodic sequences to difference equations.On the basis of these,we investigate the existence of pseudo almost periodic solutions for neutral delay differential equations with piecewise constant argument, d/(dt)(y(t)+py(t-1))=qy(2[(t+1)/2])+g(t,y(t),([t])). 展开更多
关键词 Pseudo almost periodic solutions Pseudo almost periodic sequences Neutral delay equation piecewise constant argument
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NECESSARY AND SUFFICIENT CONDITIONS FOR THE OSCILLATION OF A DELAY LOGISTIC EQUATION WITH CONTINUOUS AND PIECEWISE CONSTANT ARGUMENTS 被引量:4
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作者 Wang Youbin Yan Jurang 《Annals of Differential Equations》 2005年第3期435-438,共4页
In this paper, we obtain some necessary and sufficient conditions for the oscillation of all positive solutions of a delay Logistic equation with continuous and piecewise constant arguments about the positive equilibr... In this paper, we obtain some necessary and sufficient conditions for the oscillation of all positive solutions of a delay Logistic equation with continuous and piecewise constant arguments about the positive equilibrium. 展开更多
关键词 OSCILLATION Logistic equation continuous and piecewise constant argument
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Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments 被引量:2
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作者 Yidan Geng Minghui Song +1 位作者 Yulan Lu Mingzhu Liu 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2021年第1期194-218,共25页
In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz c... In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition.The order of convergence is obtained.Moreover,we show that the truncated EM method can preserve the exponential mean square stability of SDEPCAs.Numerical examples are provided to support our conclusions. 展开更多
关键词 Stochastic differential equations with piecewise continuous argument local Lips-chitz condition Khasminskii-type condition truncated Euler-Maruyama method convergence and stability
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ON ALMOST PERIODIC SOLUTIONS TO THIRD-ORDER NEUTRAL DELAY-DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT 被引量:3
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作者 Rongkun Zhuang Hongwu Wu 《Annals of Differential Equations》 2013年第1期114-120,共7页
We present some conditions for the existence and uniqueness of almost periodic solutions to third order neutral delay-differential equations with piecewise constant.
关键词 almost periodic solutions neutral delay equation piecewise constant argument
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一类带有分段常数变元的线性时滞微分方程的振动判据
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作者 张冰清 寇春海 《东华大学学报(自然科学版)》 CAS 北大核心 2024年第2期170-180,共11页
针对一类带有分段变元的线性时滞微分方程,在系数缓慢变化的情形下,利用Bolzano-Weierstrass定理,建立判定其振动性的充分条件,将已有的下极限型条件改进为上极限型条件,进而可以判定部分原先所不能判定的方程的振动性,并采用2个例子证... 针对一类带有分段变元的线性时滞微分方程,在系数缓慢变化的情形下,利用Bolzano-Weierstrass定理,建立判定其振动性的充分条件,将已有的下极限型条件改进为上极限型条件,进而可以判定部分原先所不能判定的方程的振动性,并采用2个例子证明其有效性。 展开更多
关键词 线性时滞微分方程 分段常数变元 振动
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