In this paper,some sufficient conditions are obtained for the oscillation for solutions of systems of highd order partial differential equations of neutral type.
Applying the frequency domain method and the inequality method, we discussed the unconditional stability problem of the multigroup multidelays neutral type linear constant continuous control system, and obtained some ...Applying the frequency domain method and the inequality method, we discussed the unconditional stability problem of the multigroup multidelays neutral type linear constant continuous control system, and obtained some sufficient conditions.展开更多
Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis.The oscillations problems for the neutral parabolic systems were con...Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis.The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.展开更多
In this paper we choose the symmetric positive definite solutionof Riccati matrix algebraic equation and,construct a positive defini-tequadratic form V-function and,use Lyapunov deco mpositionequivalence method founde...In this paper we choose the symmetric positive definite solutionof Riccati matrix algebraic equation and,construct a positive defini-tequadratic form V-function and,use Lyapunov deco mpositionequivalence method founded by Liu Yong-qing to obtain the condi-tions of the asymptotic stability of the solution of neutral typelinear large scale control system,the estimate formula of thedecom posing coefficients and time delay are also given.展开更多
In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)...In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)))g(x′(t))=0are obtained.展开更多
In this paper, oscillatory properties of all solutions for neutral type impulsive hyperbolic equations with several delays under the Robin boundary condition are investigated and several new sufficient conditions for ...In this paper, oscillatory properties of all solutions for neutral type impulsive hyperbolic equations with several delays under the Robin boundary condition are investigated and several new sufficient conditions for oscillation are presented.展开更多
Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fo...Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fourier series. Some new necessary and sufficient conditions of existence and uniqueness of 2 T-periodic solutions for the equation are obtained. The main result is used widely. It contains results in some correlation paper for its special case, improves and extends the main results in them. Existence of periodic solution for the equation in larger number of particular case can be checked by using the result, but cannot be checked in another paper. In other words, the main result in this paper is most generalized for (1) the better result cannot be found by using the same method.展开更多
The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and alm...The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and almost exponential stability for the uncertain neutral stochastic differential systems with delay. An example is given to verify the effectiveness of obtained results.展开更多
The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△（an△^2（xn＋bnxn-τ1＋cnxn＋τ2））＋qnx^βn＋1-σ1＋pnx^^βn...The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△（an△^2（xn＋bnxn-τ1＋cnxn＋τ2））＋qnx^βn＋1-σ1＋pnx^^βn＋1＋σ2=0,where （an）, （bn}, （cn}, （qn} and （pn} are positive real sequences, β is a ratio of odd positive integers, τ1, τ2, and σ2 are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results.展开更多
The problem of periodic solutions for nonlinear neutral functional differential equations d/dt D(t,x(t)) = f(t,xt) is discussed using coincidence theory. A new result on the d t existence of periodic solutions is obta...The problem of periodic solutions for nonlinear neutral functional differential equations d/dt D(t,x(t)) = f(t,xt) is discussed using coincidence theory. A new result on the d t existence of periodic solutions is obtained.展开更多
On the study of the solutions to the partial functional differential equations,there existsome good results.However,for the related neutral-type systems,there seems to be noresult appearing to deal with the stability ...On the study of the solutions to the partial functional differential equations,there existsome good results.However,for the related neutral-type systems,there seems to be noresult appearing to deal with the stability of solutions due to the difficulties of study.In this note,we will make some explorations by constructing several auxillary functionalsand combining L_p-estimates to analyze the stability of solutions to a class of展开更多
文摘In this paper,some sufficient conditions are obtained for the oscillation for solutions of systems of highd order partial differential equations of neutral type.
文摘Applying the frequency domain method and the inequality method, we discussed the unconditional stability problem of the multigroup multidelays neutral type linear constant continuous control system, and obtained some sufficient conditions.
文摘Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis.The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.
基金The Project was supported by the Science Fund of the Chinese Natural Science.
文摘In this paper we choose the symmetric positive definite solutionof Riccati matrix algebraic equation and,construct a positive defini-tequadratic form V-function and,use Lyapunov deco mpositionequivalence method founded by Liu Yong-qing to obtain the condi-tions of the asymptotic stability of the solution of neutral typelinear large scale control system,the estimate formula of thedecom posing coefficients and time delay are also given.
基金Supported by National Basic Research Program of China （973 Program） （2009CB320601）, National Natural Science Foundation of China （50977008, 60774048）, and the Program for Cheung Kong Scholars
文摘In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)))g(x′(t))=0are obtained.
文摘In this paper, oscillatory properties of all solutions for neutral type impulsive hyperbolic equations with several delays under the Robin boundary condition are investigated and several new sufficient conditions for oscillation are presented.
文摘Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fourier series. Some new necessary and sufficient conditions of existence and uniqueness of 2 T-periodic solutions for the equation are obtained. The main result is used widely. It contains results in some correlation paper for its special case, improves and extends the main results in them. Existence of periodic solution for the equation in larger number of particular case can be checked by using the result, but cannot be checked in another paper. In other words, the main result in this paper is most generalized for (1) the better result cannot be found by using the same method.
基金Project supported by the National Natural Science Foundation of China (No.60574025)the Natural Science Foundation of Hubei Province of China (Nos.2004ABA055, D200613002)the Natural Science Foundation of China Three Gorges University.
文摘The LaSalle-type theorem for the neutral stochastic differential equations with delay is established for the first time and then applied to propose algebraic criteria of the stochastically asymptotic stability and almost exponential stability for the uncertain neutral stochastic differential systems with delay. An example is given to verify the effectiveness of obtained results.
文摘The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△（an△^2（xn＋bnxn-τ1＋cnxn＋τ2））＋qnx^βn＋1-σ1＋pnx^^βn＋1＋σ2=0,where （an）, （bn}, （cn}, （qn} and （pn} are positive real sequences, β is a ratio of odd positive integers, τ1, τ2, and σ2 are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results.
基金The research supported by National Natural Science Foundation of China
文摘The problem of periodic solutions for nonlinear neutral functional differential equations d/dt D(t,x(t)) = f(t,xt) is discussed using coincidence theory. A new result on the d t existence of periodic solutions is obtained.
基金supported by the National Natural Science Foundation of China.
文摘On the study of the solutions to the partial functional differential equations,there existsome good results.However,for the related neutral-type systems,there seems to be noresult appearing to deal with the stability of solutions due to the difficulties of study.In this note,we will make some explorations by constructing several auxillary functionalsand combining L_p-estimates to analyze the stability of solutions to a class of
