In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transf...In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.展开更多
Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and glob...Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.展开更多
A compact quantum metric space is a complete order unit space A endowed with a Lipnorm L.We give some characterizations of almost periodic type group actions on a compact quantum metric space(A,L)by means of several k...A compact quantum metric space is a complete order unit space A endowed with a Lipnorm L.We give some characterizations of almost periodic type group actions on a compact quantum metric space(A,L)by means of several kinds of subsets of A,its induced equicontinuous actions on several important subsets of the dual Banach space A*,and the Lip-norm L with its induced metric space structures on the state space S(A)of A.展开更多
In this paper, the spectrum relation of almost periodic solution for the equation (x(t) +px(t - 1))" = qx([t]) + f(Q is investigated. Although this has been discussed in an article, some counterexamples ar...In this paper, the spectrum relation of almost periodic solution for the equation (x(t) +px(t - 1))" = qx([t]) + f(Q is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some part of the spectrum inclusion in that article is not correct. The key point which causes such problem is found out. A new statement is formulated and proved.展开更多
This paper presents the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations, by using a fixed point theorem in the mixed monotone operators (Ma, Y.: On a cl...This paper presents the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations, by using a fixed point theorem in the mixed monotone operators (Ma, Y.: On a class of mixed monotone operators and a kind of two-point bounded value problem. Indian J. Math., 41(2), 211-220 (1999]]. Some known results are operators.展开更多
In this paper, in the sense of the definition of almost periodicity given by H.Bohr using fixed-point principle, we investigate the existence and uniqueness of quadratic mean almost periodic solutions to semi-linear s...In this paper, in the sense of the definition of almost periodicity given by H.Bohr using fixed-point principle, we investigate the existence and uniqueness of quadratic mean almost periodic solutions to semi-linear stochastic integro-differential evolution equations associated with abstract Volterra equations. Some examples are also given to illustrate our theory.展开更多
This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so...This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called "Acquistapace–Terreni" conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.展开更多
By applying the properties of almost periodic function and exponential dichotomy of linear system as well as Banach fixed point theorem,we establish the conditions for the existence and uniqueness of square-mean almos...By applying the properties of almost periodic function and exponential dichotomy of linear system as well as Banach fixed point theorem,we establish the conditions for the existence and uniqueness of square-mean almost periodic solution to some stochastic functional differential equations.展开更多
文摘In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.
基金Supported by the NNSF of China(10671021)the SRF of Hunan Provincial Education Department(09C388)
文摘Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.
基金Supported by National Natural Science Foundation of China(Grant No.11801177)Postdoctoral Science Foundation of China(Grant No.2020M671471)Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000)。
文摘A compact quantum metric space is a complete order unit space A endowed with a Lipnorm L.We give some characterizations of almost periodic type group actions on a compact quantum metric space(A,L)by means of several kinds of subsets of A,its induced equicontinuous actions on several important subsets of the dual Banach space A*,and the Lip-norm L with its induced metric space structures on the state space S(A)of A.
基金The first author is supported by NPU Foundation for Fundamental Research (NPU-FFR-JC20100220) the second author is supported by National Natural Science Foundation (Grant No. 11031002) and RFDP the third author is supported by National Natural Science Foundation (Grant No. 11071048 )
文摘In this paper, the spectrum relation of almost periodic solution for the equation (x(t) +px(t - 1))" = qx([t]) + f(Q is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some part of the spectrum inclusion in that article is not correct. The key point which causes such problem is found out. A new statement is formulated and proved.
基金the National Natural Science Foundation of China (10371010) and RFDP
文摘This paper presents the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations, by using a fixed point theorem in the mixed monotone operators (Ma, Y.: On a class of mixed monotone operators and a kind of two-point bounded value problem. Indian J. Math., 41(2), 211-220 (1999]]. Some known results are operators.
文摘In this paper, in the sense of the definition of almost periodicity given by H.Bohr using fixed-point principle, we investigate the existence and uniqueness of quadratic mean almost periodic solutions to semi-linear stochastic integro-differential evolution equations associated with abstract Volterra equations. Some examples are also given to illustrate our theory.
基金Supported by National Natural Science Foundation of China(Grant Nos.11201266 and 11171191)TianyuanYouth Foundation of National Natural Science Foundation of China(Grant Nos.11026150 and 11026098)Excellent Youth Foundation of Shandong Institute of Business and Technology
文摘This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called "Acquistapace–Terreni" conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.
基金partially supported by the NNSF of China(No.11171191)the NSF of Shandong Province(No.ZR2010AL011)
文摘By applying the properties of almost periodic function and exponential dichotomy of linear system as well as Banach fixed point theorem,we establish the conditions for the existence and uniqueness of square-mean almost periodic solution to some stochastic functional differential equations.