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)
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
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
