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
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
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
In this paper,some sufficient conditions are obtained for the oscillation for solutions of systems of highd order partial differential equations of neutral type.
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
The principle aim of this paper is to explore the existence of periodic solution of neural networks model with neutral delay. Sufficient and realistic conditions are obtained by means of an abstract continuous theorem...The principle aim of this paper is to explore the existence of periodic solution of neural networks model with neutral delay. Sufficient and realistic conditions are obtained by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.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. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j...In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j(u(x,σ_j(t))) =a(t)△u(x,t)+sun form k=1 to n ak(t)△u(x,pk(t)), (x,t)∈Ω×R_+≡G where △ is the Laplacian in Euclidean N-space R^N, R_+=(0, ∞) and Ω is a bounded domain in R^N with a piecewise smooth boundary Ω.展开更多
Neutral hyperbolic differential equations with continuous distributed devia-ting arguments are studied, and sufficient conditions for each solution of the boundary value problem to be oscillatory in a cylindrical doma...Neutral hyperbolic differential equations with continuous distributed devia-ting arguments are studied, and sufficient conditions for each solution of the boundary value problem to be oscillatory in a cylindrical domain are obtained.展开更多
The models of competitive neural network(CNN)was in recent past proposed to describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications,where there are two types of memories:Long-term mem...The models of competitive neural network(CNN)was in recent past proposed to describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications,where there are two types of memories:Long-term memories(LTM)and short-term memories(STM),LTM presents unsupervised and slow synaptic modifications and STM characterize the fast neural activity.This paper is concerned with a class of neutral type CNN’s with mixed delay and D operator.By employing the appropriate differential inequality theory,some sufficient conditions are given to ensure that all solutions of the model converge exponentially to zero vector.Finally,an illustrative example is also given at the end of this paper to show the effectiveness of the proposed results.展开更多
In this paper, we establish some new oscillation criteria for second order difference equations of neutral type with mixed arguments. We extend some known oscillation criteria for second order difference equations.
Sufficient conditions are obtained for the oscillation of the solutions to nonlinear parabolic differential equations of neutral type in the form of where Ω is a bounded domain in Rn with a piecewise smooth boundary.
The serum samples and corresponding cervical swabs were collected from 50 women with genital warts from Tianjin city,China.The neutralizing antibodies against HPV-16,-18,-58,-45,-6 and-11 in serum samples were tested ...The serum samples and corresponding cervical swabs were collected from 50 women with genital warts from Tianjin city,China.The neutralizing antibodies against HPV-16,-18,-58,-45,-6 and-11 in serum samples were tested by using pseudovirus-based neutralization assays and HPV DNAs in cervical swabs were also tested by using a typing kit that can detect 21 types of HPV.The results revealed that 36%(18/50)of sera were positive for type-specific neutralizing antibodies with a titer range of 160-2560,of which 22%(11/50),12%(6/50), 10%(5/50),4%(2/50),4%(2/50)and 2%(1/50)were against HPVs-6,-16,-18,-58,-45 and-11,respectively. Additionally,60%(30/50)of samples were HPV DNA-positive,in which the most common types detected were HPV-68(18%),HPV-16(14%),HPV-58(12%),HPV-33(8%)and HPV-6,HPV-11,HPV-18 and HPV-52(6% each).The concordance between HPV DNA and corresponding neutralizing antibodies was 56%(28/50)with a significant difference(P<0.05).The full-length sequences of five HPV types(HPV-42,-52,-53,-58 and-68) were determined and exhibited 98%-100%identities with their reported genomes.The present data may have utility for investigating the natural history of HPV infection and promote the development of HPV vaccines.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
The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equa...The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.展开更多
In this paper, we employ a fixed point theorem due to Krasnosel’skii to attain the existence of periodic solutions for neutral-type neural networks with delays on a periodic time scale. Some new sufficient conditions...In this paper, we employ a fixed point theorem due to Krasnosel’skii to attain the existence of periodic solutions for neutral-type neural networks with delays on a periodic time scale. Some new sufficient conditions are established to show that there exists a unique periodic solution by the contraction mapping principle.展开更多
This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several differen...This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.展开更多
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.
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.
文摘The principle aim of this paper is to explore the existence of periodic solution of neural networks model with neutral delay. Sufficient and realistic conditions are obtained by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.
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 the National Natural Science Foundation of China
文摘In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j(u(x,σ_j(t))) =a(t)△u(x,t)+sun form k=1 to n ak(t)△u(x,pk(t)), (x,t)∈Ω×R_+≡G where △ is the Laplacian in Euclidean N-space R^N, R_+=(0, ∞) and Ω is a bounded domain in R^N with a piecewise smooth boundary Ω.
文摘Neutral hyperbolic differential equations with continuous distributed devia-ting arguments are studied, and sufficient conditions for each solution of the boundary value problem to be oscillatory in a cylindrical domain are obtained.
文摘The models of competitive neural network(CNN)was in recent past proposed to describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications,where there are two types of memories:Long-term memories(LTM)and short-term memories(STM),LTM presents unsupervised and slow synaptic modifications and STM characterize the fast neural activity.This paper is concerned with a class of neutral type CNN’s with mixed delay and D operator.By employing the appropriate differential inequality theory,some sufficient conditions are given to ensure that all solutions of the model converge exponentially to zero vector.Finally,an illustrative example is also given at the end of this paper to show the effectiveness of the proposed results.
基金Project supported by Natural Science Foundation of Educational Department of Shandong Province(03P51)(J04A60).
文摘In this paper, we establish some new oscillation criteria for second order difference equations of neutral type with mixed arguments. We extend some known oscillation criteria for second order difference equations.
文摘Sufficient conditions are obtained for the oscillation of the solutions to nonlinear parabolic differential equations of neutral type in the form of where Ω is a bounded domain in Rn with a piecewise smooth boundary.
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The serum samples and corresponding cervical swabs were collected from 50 women with genital warts from Tianjin city,China.The neutralizing antibodies against HPV-16,-18,-58,-45,-6 and-11 in serum samples were tested by using pseudovirus-based neutralization assays and HPV DNAs in cervical swabs were also tested by using a typing kit that can detect 21 types of HPV.The results revealed that 36%(18/50)of sera were positive for type-specific neutralizing antibodies with a titer range of 160-2560,of which 22%(11/50),12%(6/50), 10%(5/50),4%(2/50),4%(2/50)and 2%(1/50)were against HPVs-6,-16,-18,-58,-45 and-11,respectively. Additionally,60%(30/50)of samples were HPV DNA-positive,in which the most common types detected were HPV-68(18%),HPV-16(14%),HPV-58(12%),HPV-33(8%)and HPV-6,HPV-11,HPV-18 and HPV-52(6% each).The concordance between HPV DNA and corresponding neutralizing antibodies was 56%(28/50)with a significant difference(P<0.05).The full-length sequences of five HPV types(HPV-42,-52,-53,-58 and-68) were determined and exhibited 98%-100%identities with their reported genomes.The present data may have utility for investigating the natural history of HPV infection and promote the development of HPV vaccines.
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
基金Sponsored by HUST Foundation(0125011017)the National NSFC under grant(70671047)
文摘The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.
文摘In this paper, we employ a fixed point theorem due to Krasnosel’skii to attain the existence of periodic solutions for neutral-type neural networks with delays on a periodic time scale. Some new sufficient conditions are established to show that there exists a unique periodic solution by the contraction mapping principle.
基金Supported by NSFC (11001091)Chinese UniversityResearch Foundation (2010MS129)
文摘This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.
