In this paper, we consider the existence and uniqueness of the solutions which are pseudo almost automorphic in distribution for a class of non-autonomous stochastic differential equations in a Hilbert space. In concl...In this paper, we consider the existence and uniqueness of the solutions which are pseudo almost automorphic in distribution for a class of non-autonomous stochastic differential equations in a Hilbert space. In conclusion, we use the Banach contraction mapping principle and exponential dichotomy property to obtain our main results.展开更多
In this paper, we study the Poisson stability(in particular, stationarity, periodicity, quasiperiodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, ps...In this paper, we study the Poisson stability(in particular, stationarity, periodicity, quasiperiodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, pseudo periodicity, almost recurrence in the sense of Bebutov, pseudo recurrence, Poisson stability) of motions for monotone nonautonomous dynamical systems and of solutions for some classes of monotone nonautonomous evolution equations(ODEs, FDEs and parabolic PDEs). As a byproduct, some of our results indicate that all the trajectories of monotone systems converge to the above mentioned Poisson stable trajectories under some suitable conditions, which is interesting in its own right for monotone dynamics.展开更多
This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear functional integro-differential stochastic evolution equations in real separable Hilbert spaces. Under some suitable a...This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear functional integro-differential stochastic evolution equations in real separable Hilbert spaces. Under some suitable assumptions, the existence, uniqueness and asymptotic stability of the square-mean almost automorphic mild solution to some stochastic differential equations are established. As an application, we analyze the almost automorphic mild solution to some stochastic partial functional differential equation which turns out to be in good agreement with our abstract results.展开更多
In this paper,a new and general existence and uniqueness theorem of almost automorphic mild solutions is obtained for some fractional delay differential equations,using sectorial operators and the Banach contraction p...In this paper,a new and general existence and uniqueness theorem of almost automorphic mild solutions is obtained for some fractional delay differential equations,using sectorial operators and the Banach contraction principle.展开更多
In this paper,we consider a semilinear difference equation in a Banach space.Under some suitable conditions on f,we prove the existence and uniqueness of a weighted pseudo almost automorphic sequence solution to the e...In this paper,we consider a semilinear difference equation in a Banach space.Under some suitable conditions on f,we prove the existence and uniqueness of a weighted pseudo almost automorphic sequence solution to the equation.展开更多
In this paper,we aim to study the existence and uniqueness of square-mean almost automorphic mild solution to a stochastic delay equation under some suitable assumptions imposed on its coefficients.As an application,a...In this paper,we aim to study the existence and uniqueness of square-mean almost automorphic mild solution to a stochastic delay equation under some suitable assumptions imposed on its coefficients.As an application,almost automorphic mild solutions to a class of stochastic partial functional differential equations are analyzed,which shows the feasibility of our results.展开更多
基金The Undergraduate Research Training Program Grant(J1030101)the NSF(11271151)of China
文摘In this paper, we consider the existence and uniqueness of the solutions which are pseudo almost automorphic in distribution for a class of non-autonomous stochastic differential equations in a Hilbert space. In conclusion, we use the Banach contraction mapping principle and exponential dichotomy property to obtain our main results.
基金supported by National Natural Science Foundation of China (Grant Nos. 11271151 and 11522104)the Startup and Xinghai Jieqing Funds from Dalian University of Technology
文摘In this paper, we study the Poisson stability(in particular, stationarity, periodicity, quasiperiodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, pseudo periodicity, almost recurrence in the sense of Bebutov, pseudo recurrence, Poisson stability) of motions for monotone nonautonomous dynamical systems and of solutions for some classes of monotone nonautonomous evolution equations(ODEs, FDEs and parabolic PDEs). As a byproduct, some of our results indicate that all the trajectories of monotone systems converge to the above mentioned Poisson stable trajectories under some suitable conditions, which is interesting in its own right for monotone dynamics.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11201266 and 11171191)Tianyuan Youth Foundation of National Natural Science Foundation of China(Grant Nos.11026150 and 11026098)+2 种基金China Postdoctoral Science Foundation(Grant No.2013M541534)Shanghai Postdoctoral Science Foundation(Grant No.13R21415600)Excellent Youth Foundation of SDIBT
文摘This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear functional integro-differential stochastic evolution equations in real separable Hilbert spaces. Under some suitable assumptions, the existence, uniqueness and asymptotic stability of the square-mean almost automorphic mild solution to some stochastic differential equations are established. As an application, we analyze the almost automorphic mild solution to some stochastic partial functional differential equation which turns out to be in good agreement with our abstract results.
基金supported by the NNSF of China(Grant No.11026098,11026150 and11171191)
文摘In this paper,a new and general existence and uniqueness theorem of almost automorphic mild solutions is obtained for some fractional delay differential equations,using sectorial operators and the Banach contraction principle.
基金supported by Tianyuan Youth Foundations for Mathematics of NSFC(Grant No.11026150,11026098)the Doctor Scientific Research Foundation of Shandong Institute of Business and Technology(Grant No.521-014-306131)
文摘In this paper,we consider a semilinear difference equation in a Banach space.Under some suitable conditions on f,we prove the existence and uniqueness of a weighted pseudo almost automorphic sequence solution to the equation.
基金Partially supported by the NNSF of China(Grant No.11026150,11026098 and 11171191)
文摘In this paper,we aim to study the existence and uniqueness of square-mean almost automorphic mild solution to a stochastic delay equation under some suitable assumptions imposed on its coefficients.As an application,almost automorphic mild solutions to a class of stochastic partial functional differential equations are analyzed,which shows the feasibility of our results.
