In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization an...In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization and continuation of the recent results on this issue.In the end,an example is given to show the application of the results.展开更多
In this paper we study the oscillation and asymptotic behavior of third order delay differential equations with impulses. Some new sufficient conditions which guarantee that every solution is oscillatory or converges ...In this paper we study the oscillation and asymptotic behavior of third order delay differential equations with impulses. Some new sufficient conditions which guarantee that every solution is oscillatory or converges to zero are obtained. Three examples are also given to illustrate our main results.展开更多
The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses x’(t)+sum from i=1 to n(p_i(t)f(x(t-т_i))=h(t)). t≠t_k, x(t_k^+)...The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses x’(t)+sum from i=1 to n(p_i(t)f(x(t-т_i))=h(t)). t≠t_k, x(t_k^+)-x(t_k)=b_kx(t_k). Our results. which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations. improve and generalize the known results recently obtained in [8].展开更多
Sufficient conditions are obtained respectively for tending to zero of the nonoscillatory solutions of equation with impulses and for tending to infinite of every nonoscillatory solution. Conditions are also obtained ...Sufficient conditions are obtained respectively for tending to zero of the nonoscillatory solutions of equation with impulses and for tending to infinite of every nonoscillatory solution. Conditions are also obtained for all solutions to be oscillatory when the equation is of oscillating coefficients.展开更多
In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic ...In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results of the existence of positive periodic solution about the equation are obtained.展开更多
In the present paper sufficient conditions are obtained for the stability of the zero solution of a nonlinear delay differential equation caused by impulses.
In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differen...In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differential equations with nonlinear diffusion coefficient are investigated.Sufficient conditions for oscillations of such equations are obtained.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
In this paper, we will study generic oscillation and generic nonoscillation of first order impulsive delay differential equations. A necessary and sufficient condition and some sufficient conditions are obtained for b...In this paper, we will study generic oscillation and generic nonoscillation of first order impulsive delay differential equations. A necessary and sufficient condition and some sufficient conditions are obtained for both phenomena based on the root of characteristic equation.展开更多
In this paper,some sufficient conditions for oscillation of a first order delay differential equation with oscillating coefficients of the formx′(t)+p(t)x(t-τ)=0are established,which improve and generalize some of t...In this paper,some sufficient conditions for oscillation of a first order delay differential equation with oscillating coefficients of the formx′(t)+p(t)x(t-τ)=0are established,which improve and generalize some of the known results in the literature.展开更多
A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations （FDEs）, so...A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations （FDEs）, some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.展开更多
In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation ar...In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation are established.展开更多
The aim of this paper is to the discussion of the exponential stability of a class of impulsive neutral stochastic functional differential equations with Markovian switching.Under the influence of impulsive disturbanc...The aim of this paper is to the discussion of the exponential stability of a class of impulsive neutral stochastic functional differential equations with Markovian switching.Under the influence of impulsive disturbance,the solution for the system is discontinuous.By using the Razumikhin technique and stochastic analysis approaches,as well as combining the idea of mathematical induction and classification discussion,some sufficient conditions for the pth moment exponential stability and almost exponential stability of the systems are obtained.The stability conclusion is full time-delay.The results show that impulse,the point distance of impulse and Markovain switching affect the stability for the system.Finally,two examples are provided to illustrate the effectiveness of the results proposed.展开更多
In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions fo...In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.展开更多
In this paper, a class of delay differential equations with nonlinear impulsive control is discussed. Based on the nonsmooth analysis, criteria of stability are obtained for delay differential equations with nonlinear...In this paper, a class of delay differential equations with nonlinear impulsive control is discussed. Based on the nonsmooth analysis, criteria of stability are obtained for delay differential equations with nonlinear impulses control under certain conditions. These criteria can be applied to some neural network models. At the end of the paper, two examples are provided to illustrate the feasibility and effectiveness of the proposed results.展开更多
In this paper, we consider the uniform stability and uniformly asymptotical stability of nonlinear impulsive infinite delay differential equations. Instead of putting all components of the state variable x in one Lyap...In this paper, we consider the uniform stability and uniformly asymptotical stability of nonlinear impulsive infinite delay differential equations. Instead of putting all components of the state variable x in one Lyapunov function, several Lyapunov-Razumikhin functions of partial components of the state variable x are used so that the conditions ensuring that stability are simpler and less restrictive; moreover, examples are discussed to illustrate the advantage of the results obtained.展开更多
This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theori...This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theories of evolution systems,we prove some existence theorems. As an application,an example is also given to illustrate the obtained results.展开更多
基金National Natural Science Foundation of China(No.10971139)Fundamental Research Funds for the Central Universities,China(No.B081)
文摘In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization and continuation of the recent results on this issue.In the end,an example is given to show the application of the results.
文摘In this paper we study the oscillation and asymptotic behavior of third order delay differential equations with impulses. Some new sufficient conditions which guarantee that every solution is oscillatory or converges to zero are obtained. Three examples are also given to illustrate our main results.
基金This work is supported by the NNSF of China and the NSF of Hunan Province
文摘The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses x’(t)+sum from i=1 to n(p_i(t)f(x(t-т_i))=h(t)). t≠t_k, x(t_k^+)-x(t_k)=b_kx(t_k). Our results. which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations. improve and generalize the known results recently obtained in [8].
文摘Sufficient conditions are obtained respectively for tending to zero of the nonoscillatory solutions of equation with impulses and for tending to infinite of every nonoscillatory solution. Conditions are also obtained for all solutions to be oscillatory when the equation is of oscillating coefficients.
基金This research had been supported by the National Nature Science Foundation of China (No. 10241005)the Key Program of Ministry of Education of China (No. 205068).
文摘In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results of the existence of positive periodic solution about the equation are obtained.
基金This work is partially supported by NNSF of China and EYTF of National Educational Committee
文摘In the present paper sufficient conditions are obtained for the stability of the zero solution of a nonlinear delay differential equation caused by impulses.
基金Supported by the Natural Science Foundation of China(10471086)Supported by the Science Research Foundation of Department of Education of Hunan Province(07C164)
文摘In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differential equations with nonlinear diffusion coefficient are investigated.Sufficient conditions for oscillations of such equations are obtained.
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.
文摘In this paper, we will study generic oscillation and generic nonoscillation of first order impulsive delay differential equations. A necessary and sufficient condition and some sufficient conditions are obtained for both phenomena based on the root of characteristic equation.
基金This project is supported by the NNSF of China (19831030).
文摘In this paper,some sufficient conditions for oscillation of a first order delay differential equation with oscillating coefficients of the formx′(t)+p(t)x(t-τ)=0are established,which improve and generalize some of the known results in the literature.
基金supported by the National Natural Science Foundation of China (Grant Nos 60534010,60774048,60728307,60804006 and 60521003)the National High Technology Research and Development Program of China (Grant No 2006AA04Z183)+1 种基金Liaoning Provincial Natural Science Foundation,China (Grant No 20062018)111 Project (Grant No B08015)
文摘A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations （FDEs）, some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.
基金This work is supported by National Natural Science Foundation of China (40373003 and 40372121).
文摘In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation are established.
基金This research was supported by the National Nature Science Foundation of China under Grant No.11571245Young Crop Project of Sichuan University under Grant No.2020SCUNL111.
文摘The aim of this paper is to the discussion of the exponential stability of a class of impulsive neutral stochastic functional differential equations with Markovian switching.Under the influence of impulsive disturbance,the solution for the system is discontinuous.By using the Razumikhin technique and stochastic analysis approaches,as well as combining the idea of mathematical induction and classification discussion,some sufficient conditions for the pth moment exponential stability and almost exponential stability of the systems are obtained.The stability conclusion is full time-delay.The results show that impulse,the point distance of impulse and Markovain switching affect the stability for the system.Finally,two examples are provided to illustrate the effectiveness of the results proposed.
基金Supported by the National Natural Science Foundation of China(10471086).
文摘In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.
基金supported by Natural Science Foundation of China under Grant Nos.10972018 and 11072013
文摘In this paper, a class of delay differential equations with nonlinear impulsive control is discussed. Based on the nonsmooth analysis, criteria of stability are obtained for delay differential equations with nonlinear impulses control under certain conditions. These criteria can be applied to some neural network models. At the end of the paper, two examples are provided to illustrate the feasibility and effectiveness of the proposed results.
基金Supported by the National Natural Science Foundation of China(Nos.11101373,61374077 and 11271333)the Natural Science Foundation of Zhejiang Province of China(No.LY14A010008)
文摘In this paper, we consider the uniform stability and uniformly asymptotical stability of nonlinear impulsive infinite delay differential equations. Instead of putting all components of the state variable x in one Lyapunov function, several Lyapunov-Razumikhin functions of partial components of the state variable x are used so that the conditions ensuring that stability are simpler and less restrictive; moreover, examples are discussed to illustrate the advantage of the results obtained.
基金Supported by NNSF of China (10901075)the Key Project of Chinese Ministry of Education (210226)+1 种基金the Scientific Research Fund of Gansu Provincial Education Department (0804-08)"Qing Lan" Talent Engineering Funds (QL-05-16A) by Lanzhou Jiaotong University
文摘This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theories of evolution systems,we prove some existence theorems. As an application,an example is also given to illustrate the obtained results.
