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 the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria...In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptoticstability in the pth mean and the pth moment exponential stability of such equations. Finally, an example isgiven to illustrate the effectiveness of our results.展开更多
This paper is concerned with the error analysis of one-leg methods when applied to nonlinear stiff Delay Differential Equations(DDEs) with a variable delay. It is proved that a one-leg method with Lagrangian linear in...This paper is concerned with the error analysis of one-leg methods when applied to nonlinear stiff Delay Differential Equations(DDEs) with a variable delay. It is proved that a one-leg method with Lagrangian linear interpolation procedure is D-convergent of oder p if and only if it is A-stable and consistent of order p in the classical sense for ODEs. The results obtained can be regarded as extension of that for DDEs with constant delay presented by Huang Chenming et al. in展开更多
Presents information on a study which focused on the numerical solution of initial value problems for systems of neutral differential equations. Adaptations of linear multistep methods; Linear stability of linear mult...Presents information on a study which focused on the numerical solution of initial value problems for systems of neutral differential equations. Adaptations of linear multistep methods; Linear stability of linear multistep method; Presentation of numerical equations.展开更多
Using the theory of existence of periodic solutions of Hamiltonian systems, it is shown that many periodic solutions of differential delay equations can be yielded from many families of periodic solutions of the coupl...Using the theory of existence of periodic solutions of Hamiltonian systems, it is shown that many periodic solutions of differential delay equations can be yielded from many families of periodic solutions of the coupled generalized Hamiltonian systems. Some sufficient conditions on the existence of periodic solutions of differential delay equations are obtained. As a corollary of our results, the conjecture of Kaplan-Yorke on the search for periodic solutions for certain special classes of scalar differential delay equations is shown to be true when f' (0) =ω> 0.展开更多
Focuses on a study which examined the numerical solution of delay differential equations (DDE). Information on the Runge-Kutta methods for DDE; Results of the D-convergence analysis of Runge-Kutta methods; Details on ...Focuses on a study which examined the numerical solution of delay differential equations (DDE). Information on the Runge-Kutta methods for DDE; Results of the D-convergence analysis of Runge-Kutta methods; Details on the equations with several delays.展开更多
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
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical result...The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.展开更多
In [4] we proved that all Gauss methods areNtau(0)-compatible for neutral delay differential equations (NDDEs) of the form y'(t) = ay(t) + by(t-tau) + cy'(t-tau), t >0, (0.1) y(t) = g(t), -tau less than or ...In [4] we proved that all Gauss methods areNtau(0)-compatible for neutral delay differential equations (NDDEs) of the form y'(t) = ay(t) + by(t-tau) + cy'(t-tau), t >0, (0.1) y(t) = g(t), -tau less than or equal to t less than or equal to 0, where a, b, c are real, tau > 0, g(t) is a continuous real valued function. In this paper we are going to use the theory of order stars to characterize the asymptotic stability properties of Gauss methods for NDDEs. And then proved that all Gauss methods are Ntau(0)-stable.展开更多
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 work was supported by the National Natural Science Foundation of China (Grant No. 10171009) Tianyuan Young Fund of China (Grant No. 10226009).
文摘In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptoticstability in the pth mean and the pth moment exponential stability of such equations. Finally, an example isgiven to illustrate the effectiveness of our results.
文摘This paper is concerned with the error analysis of one-leg methods when applied to nonlinear stiff Delay Differential Equations(DDEs) with a variable delay. It is proved that a one-leg method with Lagrangian linear interpolation procedure is D-convergent of oder p if and only if it is A-stable and consistent of order p in the classical sense for ODEs. The results obtained can be regarded as extension of that for DDEs with constant delay presented by Huang Chenming et al. in
文摘Presents information on a study which focused on the numerical solution of initial value problems for systems of neutral differential equations. Adaptations of linear multistep methods; Linear stability of linear multistep method; Presentation of numerical equations.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19731003)Science Foundation of Yunnan Province.
文摘Using the theory of existence of periodic solutions of Hamiltonian systems, it is shown that many periodic solutions of differential delay equations can be yielded from many families of periodic solutions of the coupled generalized Hamiltonian systems. Some sufficient conditions on the existence of periodic solutions of differential delay equations are obtained. As a corollary of our results, the conjecture of Kaplan-Yorke on the search for periodic solutions for certain special classes of scalar differential delay equations is shown to be true when f' (0) =ω> 0.
基金NSF of China (No.19871070) and China Postdoctoral Science Foundation.
文摘Focuses on a study which examined the numerical solution of delay differential equations (DDE). Information on the Runge-Kutta methods for DDE; Results of the D-convergence analysis of Runge-Kutta methods; Details on the equations with several delays.
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）.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos.10271100 and 10571147)
文摘The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
基金the National Natural Science Foundation of China.
文摘In [4] we proved that all Gauss methods areNtau(0)-compatible for neutral delay differential equations (NDDEs) of the form y'(t) = ay(t) + by(t-tau) + cy'(t-tau), t >0, (0.1) y(t) = g(t), -tau less than or equal to t less than or equal to 0, where a, b, c are real, tau > 0, g(t) is a continuous real valued function. In this paper we are going to use the theory of order stars to characterize the asymptotic stability properties of Gauss methods for NDDEs. And then proved that all Gauss methods are Ntau(0)-stable.
