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
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
By employing a fixed point theorem in cones,we investigate the existence of almost periodic solutions to an impulsive pure delay Logistic equation. A set of suffcient conditions for the existence of almost periodic so...By employing a fixed point theorem in cones,we investigate the existence of almost periodic solutions to an impulsive pure delay Logistic equation. A set of suffcient conditions for the existence of almost periodic solutions to the equation are obtained.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
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].
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.
文摘By employing a fixed point theorem in cones,we investigate the existence of almost periodic solutions to an impulsive pure delay Logistic equation. A set of suffcient conditions for the existence of almost periodic solutions to the equation are obtained.
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.
