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.
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.
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 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.
Xiliang Li , Xidong Sun (Dept. of Math. and Information Sciences, Shandong Institute of Business and Technology, Yantai 264005, Shandong)
This paper is concerned with the global existence and uniform boundedness of solutions for two classes of chemotaxis models in two or three dimensional spaces. Firstly, by using detailed energy estimates, special interpolation relation and uniform Gronwall inequality, we prove the global existence of uniformly bounded solutions for a class of chemotaztic systems with linear chemotactic-sensitivity terms and logistic reaction terms. Secondly, by applying detailed analytic semigroup estimates and special iteration techniques, we obtain the global existence of uniformly bounded solutions for a class of chemotactic systems with nonlinear chemotacticsensitivity terms, which extends the global existence results of [6] to other general cases.
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
