In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays o...In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays of the form （x（t）＋Bx（t-δ））＂＋Cx＇（t）＋g（x（t-τ））=p（t）.展开更多
A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for...A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.展开更多
The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions ...The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.展开更多
By using the concept of almost periodic 'sequence', that is, a real valued function on Z satisfying the Bohr almost periodic condition, sufficient conditions are obtained for the existence of almost periodic s...By using the concept of almost periodic 'sequence', that is, a real valued function on Z satisfying the Bohr almost periodic condition, sufficient conditions are obtained for the existence of almost periodic solutions of Lasota-Wazewska-type differential equations with almost periodic time dependence.展开更多
This study presents the design of both H∞ Loop Shaping Control （HLSC） and Internal Model Control （IMC） strategies for linear time delay systems. For first order time delay system, a systematic approach for weight...This study presents the design of both H∞ Loop Shaping Control （HLSC） and Internal Model Control （IMC） strategies for linear time delay systems. For first order time delay system, a systematic approach for weight selection based on the sensitivity function was proposed, then compared to the internal model control strategy. For both methods, the synthesis was based on the Pade approximation. Two cases are considered for time delay： upper or lower than system time constant. Simulation results for the proposed approaches are acceptable ever in presence of disturbances and model mismatches.展开更多
Neutral Delay Differential Equation(NDDE)is a differential problem that has regularly existed in numerous occurrences and has represented a significant role in dealing with real-life phenomena,especially on their appl...Neutral Delay Differential Equation(NDDE)is a differential problem that has regularly existed in numerous occurrences and has represented a significant role in dealing with real-life phenomena,especially on their application in biological and physiological processes.A fifth-order two-point hybrid implicit multistep block method(2PIH5)has been formulated in this research for the numerical solution of Neutral Delay Differential Equation(NDDE).A Taylor series interpolation polynomial has been implemented in the formulation of the proposed 2PIH5.The order,consistency,and zero-stability for 2PIH5 have been illustrated.The analyses of convergence and stability test have been performed and discussed.The initial value problems for the first-order NDDE with constant or proportional delay have been solved using the proposed block method.Some numerical results for the proposed method have been presented to prove the adaptability and applicability of the proposed method in solving NDDE.The proposed method is proved to be comparable with the other existing methods.It is assumed to be reliable and efficient for solving the first-order NDDE with constant or proportional delay.展开更多
基金Supported by the National Natural Science Foundation of China(No.10371034)the Hunan Provincial Natural Science Foundation of China(05JJ40009).
文摘In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for the second order neutral functional differential equation with constant delays of the form （x（t）＋Bx（t-δ））＂＋Cx＇（t）＋g（x（t-τ））=p（t）.
文摘A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.
基金Project supported by Natural Science Foundation of Guangdong (011471)Foundation for the study of Natural Science for Universities of Guangdong (0120).
文摘The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.
基金This work is partially supported by the Natural Sciences Foundation of P.R.China under Grant10061004the ABRF of Yunnan Province, P.R.China.
文摘By using the concept of almost periodic 'sequence', that is, a real valued function on Z satisfying the Bohr almost periodic condition, sufficient conditions are obtained for the existence of almost periodic solutions of Lasota-Wazewska-type differential equations with almost periodic time dependence.
文摘This study presents the design of both H∞ Loop Shaping Control （HLSC） and Internal Model Control （IMC） strategies for linear time delay systems. For first order time delay system, a systematic approach for weight selection based on the sensitivity function was proposed, then compared to the internal model control strategy. For both methods, the synthesis was based on the Pade approximation. Two cases are considered for time delay： upper or lower than system time constant. Simulation results for the proposed approaches are acceptable ever in presence of disturbances and model mismatches.
基金All authors gratefully acknowledge for the financial support by Putra Grant(project code:GP-IPS/2018/9625400)Graduate Research Fellowship(GRF)from Universiti Putra Malaysia.The authors are also thankful to the referees for their useful comments and suggestions.
文摘Neutral Delay Differential Equation(NDDE)is a differential problem that has regularly existed in numerous occurrences and has represented a significant role in dealing with real-life phenomena,especially on their application in biological and physiological processes.A fifth-order two-point hybrid implicit multistep block method(2PIH5)has been formulated in this research for the numerical solution of Neutral Delay Differential Equation(NDDE).A Taylor series interpolation polynomial has been implemented in the formulation of the proposed 2PIH5.The order,consistency,and zero-stability for 2PIH5 have been illustrated.The analyses of convergence and stability test have been performed and discussed.The initial value problems for the first-order NDDE with constant or proportional delay have been solved using the proposed block method.Some numerical results for the proposed method have been presented to prove the adaptability and applicability of the proposed method in solving NDDE.The proposed method is proved to be comparable with the other existing methods.It is assumed to be reliable and efficient for solving the first-order NDDE with constant or proportional delay.
