This article studies one dimensional viscous Camassa-Holm equation with a periodic boundary condition. The existence of the almost periodic solution is investigated by using the Galerkin method.
For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain li...For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.展开更多
This paper studies a kind of non-autonomous respiratory disease model with a lag effect.First of all,the permanence and extinction of the system are discussed by using the comparison principle and some differential in...This paper studies a kind of non-autonomous respiratory disease model with a lag effect.First of all,the permanence and extinction of the system are discussed by using the comparison principle and some differential inequality techniques.Second,it assumes that all coefficients of the system are periodic.The existence of positive periodic solutions of the system is proven,based on the continuation theorem in coincidence with the degree theory of Mawhin and Gaines.In the meantime,the global attractivity of positive periodic solutions of the system is obtained by constructing an appropriate Lyapunov functional and using the Razumikin theorem.In addition,the existence and uniform asymptotic stability of almost periodic solutions of the system are analyzed by assuming that all parameters in the model are almost periodic in time.Finally,the theoretical derivation is verified by a numerical simulation.展开更多
By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural ...By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.展开更多
In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost period...In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost periodic solution for the above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the positive almost periodic solution are derived.展开更多
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.
In this paper, we study the Logistic type equation x= a(t)x -b(t)x^2+ e(t). Under the assumptions that e(t) is small enough and a(t), b(t) are contained in some positive intervals, we prove that this equa...In this paper, we study the Logistic type equation x= a(t)x -b(t)x^2+ e(t). Under the assumptions that e(t) is small enough and a(t), b(t) are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a(t), b(t) and e(t) are periodic functions, and this solution is an almost periodic solution if a(t), b(t) and e(t) are almost periodic functions.展开更多
This article is concerned with a mathematical model of tumor growth governed by 2<sup>nd</sup> order diffusion equation . The source of mitotic inhibitor is almost periodic and time-dependent within the ti...This article is concerned with a mathematical model of tumor growth governed by 2<sup>nd</sup> order diffusion equation . The source of mitotic inhibitor is almost periodic and time-dependent within the tissue. The system is set up with the initial condition C(r, 0) = C<sub>0</sub>(r) and Robin type inhomogeneous boundary condition . Under certain conditions we show that there exists a unique solution for this model which is almost periodic.展开更多
In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generaliz...In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.展开更多
In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded ...In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded domains of R^(n) in the framework of interpolation spaces.For the linear Boussinesq system we combine the L^(p)—L^(q)-smoothing estimates and interpolation functors to prove the existence of bounded mild solutions.Then,we prove the existence of periodic solutions by invoking Massera’s principle.We also prove the existence of almost periodic solutions.Then we use the results of the linear Boussinesq system to establish the existence,uniqueness and stability of the small periodic and almost periodic solutions to the Boussinesq system using fixed point arguments and interpolation spaces.Our results cover and extend the previous ones obtained in[13,34,38].展开更多
Almost periodic oscillations appearing in high-tension electricity network are considered in this paper. By utilization of Liapunov function, the foreboding conditions that result in almost periodic oscillations are o...Almost periodic oscillations appearing in high-tension electricity network are considered in this paper. By utilization of Liapunov function, the foreboding conditions that result in almost periodic oscillations are obtained and thus the possibility of making precautions is presented.展开更多
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
In this paper, a class of non-autonomous functional integro-differential stochastic equations in a real separable Hilbert space is studied. When the operators A(t) satisfy Acquistapace-Terreni conditions, and with s...In this paper, a class of non-autonomous functional integro-differential stochastic equations in a real separable Hilbert space is studied. When the operators A(t) satisfy Acquistapace-Terreni conditions, and with some suitable assumptions, the existence and uniqueness of a square-mean almost periodic mild solution to the equations are obtained.展开更多
In this paper,the existence,uniqueness and global attractivity are discussed on almost periodic solution of SICNNs(shunting inhibitory cellular neural networks)with continuously distributed delays.By using the fixed...In this paper,the existence,uniqueness and global attractivity are discussed on almost periodic solution of SICNNs(shunting inhibitory cellular neural networks)with continuously distributed delays.By using the fixed point theorem,differential inequality technique and Lyapunov functional method,giving the new ranges of parameters,several sufficient conditions are obtained to ensure the existence,uniqueness and global attractivity of almost periodic solution.Compared with the previous studies,our methods are more effective for almost periodic solution analysis of SICNNs with continuously distributed delays.Some existing results have been improved and extended.In order to show the effectiveness of the obtained results,an example is given in this paper.展开更多
Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains.In this paper,the memristive multidirectio...Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains.In this paper,the memristive multidirectional associative memory neural networks(MAMNNs)with mixed time-varying delays are investigated in the sense of Filippov solution.First,three steps are given to prove the existence of the almost periodic solution.Two new lemmas are proposed to prove the boundness of the solution and the asymptotical almost periodicity of the solution by constructing Lyapunov function.Second,the uniqueness and global exponential stability of the almost periodic solution of memristive MAMNNs are investigated by a new Lyapunov function.The sufficient conditions guaranteeing the properties of almost periodic solution are derived based on the relevant definitions,Halanay inequality and Lyapunov function.The investigation is an extension of the research on the periodic solution and almost periodic solution of bidirectional associative memory neural networks.Finally,numerical examples with simulations are presented to show the validity of the main results.展开更多
This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions of a higher almost periodic system. We establish the sufficient conditions which guarantee the existence an...This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions of a higher almost periodic system. We establish the sufficient conditions which guarantee the existence and uniqueness and stability of almost periodic solutions of this system.展开更多
In this paper, we consider two-species n-patch almost periodic competitive systemswith diffusion, where one species can diffuse between any two of n patches, but the otheris confined to one of the patches and cannot d...In this paper, we consider two-species n-patch almost periodic competitive systemswith diffusion, where one species can diffuse between any two of n patches, but the otheris confined to one of the patches and cannot diffuse. We prove that the systems can have aunique positive almost periodic solution, which is globally uniformly asymptotically stableunder some appropriate conditions. In particular, if the system is a periodic system of period ω, it can have a positive globally uniformly asymptotically stable periodic solution ofperiod ω, which is a generalization of Theorem 4 in paper [6].展开更多
Based on the inherence theorem to the operator D(t) in [9], we investigate the stability with respect to the hull and the existence on almost periodic solutions for neutral functional differential equations (NFDE). Fo...Based on the inherence theorem to the operator D(t) in [9], we investigate the stability with respect to the hull and the existence on almost periodic solutions for neutral functional differential equations (NFDE). For periodic Eq. (1), we prove that if Eq. (1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to H.f(ξ),then Eq. (1 ) has an mω -- periodic solution p(t), for some integer m ≥1. Furthermore, we prove that if 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
The main purpose of this paper is to investigate the existence of almost periodic solutions for the Duffing differential equation.By combining the theory of exponential dichotomies with Liapunov functions,we obtain an...The main purpose of this paper is to investigate the existence of almost periodic solutions for the Duffing differential equation.By combining the theory of exponential dichotomies with Liapunov functions,we obtain an intersting result on the existence of almost periodic solutions.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
基金Supported by Natural Science Foundation of China (10471047)Natural Science Foundation of Guangdong Province (05300162)
文摘This article studies one dimensional viscous Camassa-Holm equation with a periodic boundary condition. The existence of the almost periodic solution is investigated by using the Galerkin method.
文摘For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.
基金supported by the National Natural ScienceFoundation of China(11401002,11771001)the Natural Science Foundation of Anhui Province(2008085MA02)+3 种基金the Natural Science Fund for Colleges and Universities in Anhui Province(KJ2018A0029)the Teaching Research Project of Anhui University(ZLTS2016065)the Quality engineering project of colleges and universities in Anhui Province(2020jyxm0103)the Science Foundation of Anhui Province Universities(KJ2019A005)。
文摘This paper studies a kind of non-autonomous respiratory disease model with a lag effect.First of all,the permanence and extinction of the system are discussed by using the comparison principle and some differential inequality techniques.Second,it assumes that all coefficients of the system are periodic.The existence of positive periodic solutions of the system is proven,based on the continuation theorem in coincidence with the degree theory of Mawhin and Gaines.In the meantime,the global attractivity of positive periodic solutions of the system is obtained by constructing an appropriate Lyapunov functional and using the Razumikin theorem.In addition,the existence and uniform asymptotic stability of almost periodic solutions of the system are analyzed by assuming that all parameters in the model are almost periodic in time.Finally,the theoretical derivation is verified by a numerical simulation.
基金The Soft Project (B30145) of Science and Technology of Hunan Province.
文摘By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.
基金Supported by the NNSF of China(11171135)Supported by the Jiangsu Province Innovation Project of Graduate Education(1221190037)
文摘In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost periodic solution for the above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the positive almost periodic solution are derived.
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.
文摘In this paper, we study the Logistic type equation x= a(t)x -b(t)x^2+ e(t). Under the assumptions that e(t) is small enough and a(t), b(t) are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a(t), b(t) and e(t) are periodic functions, and this solution is an almost periodic solution if a(t), b(t) and e(t) are almost periodic functions.
文摘This article is concerned with a mathematical model of tumor growth governed by 2<sup>nd</sup> order diffusion equation . The source of mitotic inhibitor is almost periodic and time-dependent within the tissue. The system is set up with the initial condition C(r, 0) = C<sub>0</sub>(r) and Robin type inhomogeneous boundary condition . Under certain conditions we show that there exists a unique solution for this model which is almost periodic.
文摘In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.
基金financially supported by the Vietnam National Foundation for Science and Technology Development under grant number 101.02-2021.04financially supported by Vietnam Ministry of Education and Training under Project B2022-BKA-06.
文摘In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded domains of R^(n) in the framework of interpolation spaces.For the linear Boussinesq system we combine the L^(p)—L^(q)-smoothing estimates and interpolation functors to prove the existence of bounded mild solutions.Then,we prove the existence of periodic solutions by invoking Massera’s principle.We also prove the existence of almost periodic solutions.Then we use the results of the linear Boussinesq system to establish the existence,uniqueness and stability of the small periodic and almost periodic solutions to the Boussinesq system using fixed point arguments and interpolation spaces.Our results cover and extend the previous ones obtained in[13,34,38].
文摘Almost periodic oscillations appearing in high-tension electricity network are considered in this paper. By utilization of Liapunov function, the foreboding conditions that result in almost periodic oscillations are obtained and thus the possibility of making precautions is presented.
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.
基金Acknowledgement This article is funded by the National Natural Science Foundation of China (11161052), Guangxi Natural Science Foundation of China (201 ljjA10044) and Guangxi Education Hall Project (201012MS183)
文摘In this paper, a class of non-autonomous functional integro-differential stochastic equations in a real separable Hilbert space is studied. When the operators A(t) satisfy Acquistapace-Terreni conditions, and with some suitable assumptions, the existence and uniqueness of a square-mean almost periodic mild solution to the equations are obtained.
文摘In this paper,the existence,uniqueness and global attractivity are discussed on almost periodic solution of SICNNs(shunting inhibitory cellular neural networks)with continuously distributed delays.By using the fixed point theorem,differential inequality technique and Lyapunov functional method,giving the new ranges of parameters,several sufficient conditions are obtained to ensure the existence,uniqueness and global attractivity of almost periodic solution.Compared with the previous studies,our methods are more effective for almost periodic solution analysis of SICNNs with continuously distributed delays.Some existing results have been improved and extended.In order to show the effectiveness of the obtained results,an example is given in this paper.
基金supported by the Beijing Municipal Natural Science Foundation(No.4202025)partially sponsored by the National Natural Science Foundation of China(No.61672070)the Beijing Municipal Education Commission(No.KZ201910005008).
文摘Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains.In this paper,the memristive multidirectional associative memory neural networks(MAMNNs)with mixed time-varying delays are investigated in the sense of Filippov solution.First,three steps are given to prove the existence of the almost periodic solution.Two new lemmas are proposed to prove the boundness of the solution and the asymptotical almost periodicity of the solution by constructing Lyapunov function.Second,the uniqueness and global exponential stability of the almost periodic solution of memristive MAMNNs are investigated by a new Lyapunov function.The sufficient conditions guaranteeing the properties of almost periodic solution are derived based on the relevant definitions,Halanay inequality and Lyapunov function.The investigation is an extension of the research on the periodic solution and almost periodic solution of bidirectional associative memory neural networks.Finally,numerical examples with simulations are presented to show the validity of the main results.
文摘This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions of a higher almost periodic system. We establish the sufficient conditions which guarantee the existence and uniqueness and stability of almost periodic solutions of this system.
文摘In this paper, we consider two-species n-patch almost periodic competitive systemswith diffusion, where one species can diffuse between any two of n patches, but the otheris confined to one of the patches and cannot diffuse. We prove that the systems can have aunique positive almost periodic solution, which is globally uniformly asymptotically stableunder some appropriate conditions. In particular, if the system is a periodic system of period ω, it can have a positive globally uniformly asymptotically stable periodic solution ofperiod ω, which is a generalization of Theorem 4 in paper [6].
文摘Based on the inherence theorem to the operator D(t) in [9], we investigate the stability with respect to the hull and the existence on almost periodic solutions for neutral functional differential equations (NFDE). For periodic Eq. (1), we prove that if Eq. (1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to H.f(ξ),then Eq. (1 ) has an mω -- periodic solution p(t), for some integer m ≥1. Furthermore, we prove that if 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.
基金This work is supported by NSF of China,No.19401013
文摘The main purpose of this paper is to investigate the existence of almost periodic solutions for the Duffing differential equation.By combining the theory of exponential dichotomies with Liapunov functions,we obtain an intersting result on the existence of almost periodic solutions.
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.