The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscilla...The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.展开更多
Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of...Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained.展开更多
Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equ...Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equation with impuls[es. J Comput Appl Math 197（2006）： 78-88] to the considered equation. Two examples are also inserted to illustrate our main results.展开更多
In this paper, a class of linear neutral differential system with distributed delay is considered. Sufficient conditions for the zero solution of the system to be uniformly stable as well as asymptotically stable are...In this paper, a class of linear neutral differential system with distributed delay is considered. Sufficient conditions for the zero solution of the system to be uniformly stable as well as asymptotically stable are obtained.展开更多
We obtain sufficient conditions for the oscillation of all solutions of the neutral equationOur results extend and improve some recent results in literature. Some examples are also given which can be investigated succ...We obtain sufficient conditions for the oscillation of all solutions of the neutral equationOur results extend and improve some recent results in literature. Some examples are also given which can be investigated successfully using our results but cannot be handled by any previous techniques or results.展开更多
In this paper,we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.
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
A new oscillation result is established for the first order neutral differential equationx(t) - px(t - (?)) + qx(t - σ) = 0.The results extends and improves some existing results in the literature.
In this article,we establish some new delay-dependent and delay-independent stability criteria for all solutions to a nonlinear neutral differential equation,using Lyapunov-Krasovskii functional.
We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such ...We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such that 0 ≤ a(t) ≤ L and展开更多
Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous ...Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature.展开更多
By means of variational structure and Z2 group index theory, we obtain infinite periodic solutions to a class of second-order neutral differential equations.
Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improv...Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improve some known results in the previous literatures.展开更多
By using the integral averaging technique, oscillating criteria for certain even order neutral differential equation with deviating arguments are established. These results extend some known oscillation criteria due t...By using the integral averaging technique, oscillating criteria for certain even order neutral differential equation with deviating arguments are established. These results extend some known oscillation criteria due to Xu and Xia.展开更多
Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set ...Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.展开更多
Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some...Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given.展开更多
In this paper we investigate the properties of the solutions of a class of second order neutral differential inequalities with distributed type deviating arguments . We apply the properties on the inequalities to obta...In this paper we investigate the properties of the solutions of a class of second order neutral differential inequalities with distributed type deviating arguments . We apply the properties on the inequalities to obtain some new criteria for all solutions of certain neutral hyperbolic partial functions differential equations to be oscillatory.展开更多
In this paper,existence and uniqueness of the solutions of the second order neutral differential equation with non-instantaneous impulses in a Hilbert space X are studied.This is followed by a brief discussion on the ...In this paper,existence and uniqueness of the solutions of the second order neutral differential equation with non-instantaneous impulses in a Hilbert space X are studied.This is followed by a brief discussion on the exact and trajectory controllability.Further,the strongly continuous cosine family of linear operators and Banach fixed point theorem are used to establish the results.Finally,an example is given to illustrate the analytical findings.展开更多
The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)...The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)=g(t) -τ≤t≤0 with τ>0 and a, b and c∈, and it is proved that the ‖B n‖ is suitably bounded, where B is the companion matrix.展开更多
文摘The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.
文摘Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained.
基金Supported by the NSF of Guangdong Province(S2011010004447,S2012040006865)
文摘Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equation with impuls[es. J Comput Appl Math 197（2006）： 78-88] to the considered equation. Two examples are also inserted to illustrate our main results.
基金Supported by the Natural Science Foundation of inner Mongolia (97118) and InnerMongolia Higher Education Science Research Prog
文摘In this paper, a class of linear neutral differential system with distributed delay is considered. Sufficient conditions for the zero solution of the system to be uniformly stable as well as asymptotically stable are obtained.
文摘We obtain sufficient conditions for the oscillation of all solutions of the neutral equationOur results extend and improve some recent results in literature. Some examples are also given which can be investigated successfully using our results but cannot be handled by any previous techniques or results.
基金Supported by the Science Foundation of Fushun Petroleum Institute
文摘In this paper,we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271380,11031002 and 11371058)Research Fund for the Doctoral Program of Higher Education(Grant No.20110003110004)+1 种基金the Grant of BeijingEducation Committee Key Project(Grant No.KZ201310028031)Natural Science Foundation of GuangdongProvince of China(Grant No.S2013010013212)
文摘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.
基金Supported by the Education Department of Hainan Province (HjKj200317).
文摘A new oscillation result is established for the first order neutral differential equationx(t) - px(t - (?)) + qx(t - σ) = 0.The results extends and improves some existing results in the literature.
文摘In this article,we establish some new delay-dependent and delay-independent stability criteria for all solutions to a nonlinear neutral differential equation,using Lyapunov-Krasovskii functional.
基金This research is supported by NNSF of China(19875083,10275032).
文摘We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such that 0 ≤ a(t) ≤ L and
文摘Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature.
基金Project supported by NNSF of China (10471155)the Foundation of the Guangdong Province Natural Science Committee (031608) a specific Foundation for PhD Specialities of Educational Department of China (20020558092).
文摘By means of variational structure and Z2 group index theory, we obtain infinite periodic solutions to a class of second-order neutral differential equations.
文摘Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improve some known results in the previous literatures.
文摘By using the integral averaging technique, oscillating criteria for certain even order neutral differential equation with deviating arguments are established. These results extend some known oscillation criteria due to Xu and Xia.
文摘Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.
文摘Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given.
文摘In this paper we investigate the properties of the solutions of a class of second order neutral differential inequalities with distributed type deviating arguments . We apply the properties on the inequalities to obtain some new criteria for all solutions of certain neutral hyperbolic partial functions differential equations to be oscillatory.
文摘In this paper,existence and uniqueness of the solutions of the second order neutral differential equation with non-instantaneous impulses in a Hilbert space X are studied.This is followed by a brief discussion on the exact and trajectory controllability.Further,the strongly continuous cosine family of linear operators and Banach fixed point theorem are used to establish the results.Finally,an example is given to illustrate the analytical findings.
文摘The stability analysis of linear multistep (LM) methods is carried out under Kreiss resolvent condition when they are applied to neutral delay differential equations of the form y′(t)=ay(t)+by(t-τ)+ cy′(t- τ) y(t)=g(t) -τ≤t≤0 with τ>0 and a, b and c∈, and it is proved that the ‖B n‖ is suitably bounded, where B is the companion matrix.
