In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.
The existence of periodic solutions for a class of impulsive differential equations of mixed type is studied by constructing periodic sequence solutions of difference equations.
In this paper, the existence of almost periodic solutions to general BAM neural networks with leakage delays on time scales is first studied, by using the exponential dichotomy method of linear differential equations ...In this paper, the existence of almost periodic solutions to general BAM neural networks with leakage delays on time scales is first studied, by using the exponential dichotomy method of linear differential equations and fixed point theorem. Then, the exponential stability of almost periodic solutions to such BAM neural networks on time scales is discussed by utilizing differential inequality. Finally, an example is given to support our results in this paper and the results are up-to-date.展开更多
This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions for functional differential equations with infinite delays.The author obtains some sufficient conditions wh...This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions for functional differential equations with infinite delays.The author obtains some sufficient conditions which ganrantee the existence and uniqueness and stability of almost periodic solutions with module containment.The results extend all the results of the paper and solve the two open problems proposed in under much weaker conditions than that proposed in.展开更多
In this paper, higher dimensional periodic systems with delay of the form x′(t)=A(t,x(t))x(t)+f(t,x(t-τ)), x′(t)= grad G(x(t))+f(t,x(t-τ)) are considered. Using the coincidence degree method, some suffic...In this paper, higher dimensional periodic systems with delay of the form x′(t)=A(t,x(t))x(t)+f(t,x(t-τ)), x′(t)= grad G(x(t))+f(t,x(t-τ)) are considered. Using the coincidence degree method, some sufficient conditions to guarantee the existence of periodic solution for these systems are obtained. As an application of the results, the existence of a positive periodic solution for a logarithmic population model is proved.展开更多
In this paper,Hopfield neural networks with delays and impulses are considered.By means of mathematical analysis techniques,some sufficient conditions for the existence of positive almost periodic solutions are obtained.
By constructing almost periodic sequence solutions to difference equations, the existence of almost periodic solutions of neutral delay differential equations with piecewise constant argument $$\frac{{d^2 }}{{dt^2 }}(...By constructing almost periodic sequence solutions to difference equations, the existence of almost periodic solutions of neutral delay differential equations with piecewise constant argument $$\frac{{d^2 }}{{dt^2 }}(x(t) + px(t - 1)) = qr\left( {2\left[ {\frac{{t + 1}}{2}} \right]} \right) + g{\bf{ }}(t,x(t),x([t]))$$ is studied.展开更多
In this paper, hy using successive approximation method and fixed-point theorem, we discuss a class of infinite delay integral equation and obtain some sufficient conditions which guarantee the existence and uniquenes...In this paper, hy using successive approximation method and fixed-point theorem, we discuss a class of infinite delay integral equation and obtain some sufficient conditions which guarantee the existence and uniqueness of the periodic and almost periodic solutions of the system.展开更多
In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equ...In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equations.展开更多
Many papers have been published on the existence of periodic solutions for the Duffing equation (?)+g(x)=p(t)=p(t+2π).(1) Their main assumptions imposed on g are super-linear, sub-linear and exclude the resonance cas...Many papers have been published on the existence of periodic solutions for the Duffing equation (?)+g(x)=p(t)=p(t+2π).(1) Their main assumptions imposed on g are super-linear, sub-linear and exclude the resonance cases (see Ref. [1] and Prof. T. R. Ding’s, Prof. W.G. Ge’s recent papers). Relatively speaking, there are few papers concerning the展开更多
We present some conditions for the existence and uniqueness of almost periodic solutions to third order neutral delay-differential equations with piecewise constant.
In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization an...In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization and continuation of the recent results on this issue.In the end,an example is given to show the application of the results.展开更多
By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r &l...By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r <SUB>1</SUB> and r <SUB>2</SUB> are continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞) with are positive continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞), b <SUB>i </SUB>(i = 1, 2) is nonnegative continuous ω-periodic function in R <SUB>+</SUB> = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.展开更多
This paper deals with the uniqueness and existence of periodic solutions of neutral Volterraintegrodifferential equations (1) and (2). Some new unique existence criteria are obtained.
For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if perio...For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to then Eq.(1) has an mω-periodic solution p(t), for some integer m≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq.(1) has an almost periodic solution.展开更多
In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable...In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.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
In the present paper we investigate the number of periodic solutions of the following differential equationdydt=A 1(t)y+A 2(t)y 2+A 3(t)y 3a 0(t)+a 1(t)y+a 2(t)y 2(**)which was discussed in paper , and obtain...In the present paper we investigate the number of periodic solutions of the following differential equationdydt=A 1(t)y+A 2(t)y 2+A 3(t)y 3a 0(t)+a 1(t)y+a 2(t)y 2(**)which was discussed in paper , and obtain the theorem by the method of cross-ratio of the solutions of (**) without the traditional condition assumption that the functions A i(t),a j(t) (i=1,2,3; j=0,1,2) are differential.展开更多
In this paper, the concept of generalized ω-periodic solution is given for Riccati's equationy'=a(t)y^2+b(t)y+c(t)with perriodic coefficients, the relation between generalized ω-periodicsolutions and the cha...In this paper, the concept of generalized ω-periodic solution is given for Riccati's equationy'=a(t)y^2+b(t)y+c(t)with perriodic coefficients, the relation between generalized ω-periodicsolutions and the characteristic numbers of system x'_1=c(t)x_2, x'_2=-a(t)x_1-b(t)x_2 is indicated, andseveral necessary and sufficient conditions are given using the coefficients. Moreover, in the case of a(t)without zero, the relation between the number of continuous ω-periodic solutions of y'=a(t)y^2+b(t)y+c(t)+δand the parameter δ is given; thus the problem on the existence of continuous ω-periodic.solutions is basically solved.展开更多
基金supported by the National Natural Science Foundation of China（11371027） the Projects of Outstanding Young Talents of Universities in Anhui Province（gxyq2018116）+2 种基金 the Teaching Groups in Anhui Province（2016jxtd080,2015jxtd048） the NSF of Educational Bureau of Anhui Province（KJ2017A702,KJ2017A704） the NSF of Bozhou University（BZSZKYXM201302,BSKY201539）
文摘In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.
基金theAppliedScienceFoundationofYunnan China (97A10 16Q)
文摘The existence of periodic solutions for a class of impulsive differential equations of mixed type is studied by constructing periodic sequence solutions of difference equations.
基金Partially supported by the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities'Association(Grant No.202101BA070001-045).
文摘In this paper, the existence of almost periodic solutions to general BAM neural networks with leakage delays on time scales is first studied, by using the exponential dichotomy method of linear differential equations and fixed point theorem. Then, the exponential stability of almost periodic solutions to such BAM neural networks on time scales is discussed by utilizing differential inequality. Finally, an example is given to support our results in this paper and the results are up-to-date.
文摘This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions for functional differential equations with infinite delays.The author obtains some sufficient conditions which ganrantee the existence and uniqueness and stability of almost periodic solutions with module containment.The results extend all the results of the paper and solve the two open problems proposed in under much weaker conditions than that proposed in.
文摘In this paper, higher dimensional periodic systems with delay of the form x′(t)=A(t,x(t))x(t)+f(t,x(t-τ)), x′(t)= grad G(x(t))+f(t,x(t-τ)) are considered. Using the coincidence degree method, some sufficient conditions to guarantee the existence of periodic solution for these systems are obtained. As an application of the results, the existence of a positive periodic solution for a logarithmic population model is proved.
文摘In this paper,Hopfield neural networks with delays and impulses are considered.By means of mathematical analysis techniques,some sufficient conditions for the existence of positive almost periodic solutions are obtained.
文摘By constructing almost periodic sequence solutions to difference equations, the existence of almost periodic solutions of neutral delay differential equations with piecewise constant argument $$\frac{{d^2 }}{{dt^2 }}(x(t) + px(t - 1)) = qr\left( {2\left[ {\frac{{t + 1}}{2}} \right]} \right) + g{\bf{ }}(t,x(t),x([t]))$$ is studied.
文摘In this paper, hy using successive approximation method and fixed-point theorem, we discuss a class of infinite delay integral equation and obtain some sufficient conditions which guarantee the existence and uniqueness of the periodic and almost periodic solutions of the system.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271380and11031002)Research Fund for the Doctoral Program of Higher Education(Grant No.20110003110004)Natural Science Foundation of Guangdong Province of China(Grant No.10151601501000003)
文摘In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equations.
文摘Many papers have been published on the existence of periodic solutions for the Duffing equation (?)+g(x)=p(t)=p(t+2π).(1) Their main assumptions imposed on g are super-linear, sub-linear and exclude the resonance cases (see Ref. [1] and Prof. T. R. Ding’s, Prof. W.G. Ge’s recent papers). Relatively speaking, there are few papers concerning the
基金supported by NNSF of China (No.11271380)NSF of Guangdong Province (1015160150100003)Foundation for Distinguished Young Talents in Higher Education of Guangdong of China (No.LYM08014)
文摘We present some conditions for the existence and uniqueness of almost periodic solutions to third order neutral delay-differential equations with piecewise constant.
基金National Natural Science Foundation of China(No.10971139)Fundamental Research Funds for the Central Universities,China(No.B081)
文摘In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization and continuation of the recent results on this issue.In the end,an example is given to show the application of the results.
基金National Natural Science Foundation of China (Grant No.10071022)Mathematical Tianyuan Foudation of China (Grant No.TY10026002-01-05-03) & Shanghai Priority Academic Research.
文摘By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r <SUB>1</SUB> and r <SUB>2</SUB> are continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞) with are positive continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞), b <SUB>i </SUB>(i = 1, 2) is nonnegative continuous ω-periodic function in R <SUB>+</SUB> = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.
基金project is supported by National Natural Science Foundation of China
文摘This paper deals with the uniqueness and existence of periodic solutions of neutral Volterraintegrodifferential equations (1) and (2). Some new unique existence criteria are obtained.
文摘For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to then Eq.(1) has an mω-periodic solution p(t), for some integer m≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq.(1) has an almost periodic solution.
文摘In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.
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In the present paper we investigate the number of periodic solutions of the following differential equationdydt=A 1(t)y+A 2(t)y 2+A 3(t)y 3a 0(t)+a 1(t)y+a 2(t)y 2(**)which was discussed in paper , and obtain the theorem by the method of cross-ratio of the solutions of (**) without the traditional condition assumption that the functions A i(t),a j(t) (i=1,2,3; j=0,1,2) are differential.
文摘In this paper, the concept of generalized ω-periodic solution is given for Riccati's equationy'=a(t)y^2+b(t)y+c(t)with perriodic coefficients, the relation between generalized ω-periodicsolutions and the characteristic numbers of system x'_1=c(t)x_2, x'_2=-a(t)x_1-b(t)x_2 is indicated, andseveral necessary and sufficient conditions are given using the coefficients. Moreover, in the case of a(t)without zero, the relation between the number of continuous ω-periodic solutions of y'=a(t)y^2+b(t)y+c(t)+δand the parameter δ is given; thus the problem on the existence of continuous ω-periodic.solutions is basically solved.
