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.
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.
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.
Xiliang Li 1,2,Yuliang Han 2 1.Math.and Science College,Shanghai Normal University,Shanghai 200235
In this paper,we first investigate some basic properties of asymptotically mean almost periodic random sequences on Z + and then show some properties of asymptotically mean almost periodic solutions to random difference equations.
Xidong Sun,Baifeng Liu,Yuliang Han(College of Math.and Information Sciences,Shandong Institute of Business and Technology,Yantai 264005,Shandong)
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.
Xiliang Li 1,Fenglong Qu 2,Yuliang Han 1(1.College of Math.and Information Sciences,Shandong Institute of Business and Technology,Yantai 264005,Shandong
In this paper, we study the invariant algebraic surfaces of a system, which generalizes the Lorenz system. Using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations, we characterize all the Darboux invariants, the irreducible Darboux polynomials, the rational first integrals and the algebraic integrability of this system.
利用概周期函数和指数型二分性的性质、Ito等距公式及Banach不动点定理,给出了随机积分-微分方程dx=[A（t）x（t）＋F1（t,x（t））]dt＋sum from j=1 to m∫t-∞C（t-u）Gj（u,x（u））dW（u）＋∫t-∞B（t-u）F2（us（u））du均方概周期解的存在唯一性定理.
In this paper, we first study the properties of asymptotically almost periodic functions in probability and then prove the existence of almost periodic solutions in probability to some differential equations with random terms.
