1.

ALMOST PERIODIC SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS





《Annals of Differential Equations》,2012年第3期


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 squaremean almost periodic solution to some stochastic functional differential equations.

2.

Squaremean almost periodic solutions to some stochastic evolution equations





Xi Liang Li《数学学报(英文版)》,2014年第30卷第5期


This paper concerns the squaremean almost periodic mild solutions to a class of abstract nonautonomous functional integrodifferential stochastic evolution equations in a real separable Hilbert space. By using the socalled ＂Acquistapace–Terreni＂ conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of squaremean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integrodifferential equation is considered to illustrate the applicability of our abstract results.

3.

ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS





李国成 薛小平 宋士吉《应用数学和力学(英文版)》,2004年第25卷第2期


The periodic problem of evolution inclusion is studied and its results are used toestablish existence theorems of periodic solutions of a class of semilinear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given forthis class of semilinear differential inclusion. An application to some feedback control systems isdiscussed.

4.

POSITIVE SOLUTIONS TO SEMILINEAR SECONDORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE





《Annals of Differential Equations》,2008年第1期


In this paper,we study the existence of positive periodic solution to some second order semilinear differential equation in Banach space.By the fixed point index theory, we prove that the semilinear differential equation has two positive periodic solutions.

5.

ON THE EXISTENCE OF ALMOST PERIODIC SOLUTIONS OF SOME DELAY DIFFERENTIAL EQUATIONS





冯春华《Annals of Differential Equations》,2004年第20卷第1期


By means of exponential dichotomy, this paper investigates the existence of almost periodic solutions of some delay differential equations.

6.

EXISTENCE OF MULTIPLE POSITIVE PERIODIC SOLUTIONS TO A CLASS OF INTEGRODIFFERENTIAL EQUATION





Zhijian Yao《Annals of Differential Equations》,2011年第1期


In this paper,by the AveryHenderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integrodifferential equation. Some suficient conditions are obtained for the existence of multiple positive periodic solutions.

7.

PSEUDOALMOST PERIODIC SOLUTIONS TO SOME FUNCTIONAL DIFFERENTIAL EQUATIONS





《Annals of Differential Equations》,2010年第2期


This paper is concerned with the pseudoalmost periodic solutions to some functional differential equations. By the exponential dichotomy theory and Schauder’s fixedpoint theorem, some results on the existence and uniqueness of pseudoalmost periodic solutions to the system are obtained.

8.

泛函微分方程周期解的非回复性定理





翟延慧 黄庆道 韩月才《东北数学》,2002年第18卷第2期


nonrecurrence theorem on the existence of periodic solutions for functional differential equations is proved by employing the topological method, and some applications are given.

9.

ON ALMOST PERIODIC SOLUTIONS TO THIRDORDER NEUTRAL DELAYDIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT





Rongkun Zhuang Hongwu Wu《Annals of Differential Equations》,2013年第1期


We present some conditions for the existence and uniqueness of almost periodic solutions to third order neutral delaydifferential equations with piecewise constant.

10.

ASYMPTOTICALLY ALMOST PERIODIC FUNCTIONS IN PROBABILITY





Yuliang Han Baifeng Liu Xidong Sun Xiliang Li《Annals of Differential Equations》,2013年第1期


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.

11.

Existence and uniqueness of positive solutions of semilinear elliptic equations 被引次数：1





Qiuyi DAI~《中国科学A辑(英文版)》,2007年第50卷第8期


This paper is devoted to the study of existence,uniqueness and nondegeneracy of positive solutions of semilinear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to problems is given.We prove that if the uniqueness and nondegeneracy results are valid for positive solutions of a class of semilinear elliptic equations,then they are still valid when one perturbs the differential operator a little bit.As consequences,some uniqueness results of positive solutions under the domain perturbation are also obtained.

12.

Stability of stochastic differential equation with linear fractal noise





Junjun Liao Xiangjun Wang《Frontiers of Mathematics in China》,2014年第9卷第3期


We study a class of stochastic differential equation with linear fractal noise. By an auxiliary stochastic differential equation, we prove the existence and uniqueness of the solution under some mild assumptions. We also give some estimates of moments of the solution. The exponential stability of the solution is discussed.

13.

UNIFORM ULTIMATE BOUNDEDNESS AND PERIODIC SOLUTIONS TO NONLINEAR INTEGRODIFFERENTIAL EQUATIONS





Jiabu Dishen《Annals of Differential Equations》,2013年第1期


In this paper, the existence of periodic solution to nonlinear integrodifferential equations with infinite delay is studied in the phase space (Cg,·g). We prove that the guniformly ultimately bounded solutions implies the existence of periodic solutions using Horn’s fixed point theorem. Some known results are generalized, including the famous Yoshizawa’s theorem.

14.

PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF THE SCALAR ORDINARY DIFFERENTIAL EQUATION





Chen Yiyuan《数学年刊B辑(英文版)》,1990年第11卷第4期


This paper develops a method which enables us to study the number,existence andstability of periodic solutions and almost periodic solutions of the scalar ordinarydifferential equation.Some applications of the method are also given.

15.

FIXED POINTS AND EXPONENTIAL STABILITY OF ALMOST PERIODIC MILD SOLUTIONS TO STOCHASTIC VOLTERRALEVIN EQUATIONS





Tong Ouyang Weiguo Liu《Annals of Differential Equations》,2015年第2期


In this paper, we consider stochastic VolterraLevin equations. Based on semigroup of operators and fixed point method, under some suitable assumptions to ensure the existence and stability of pthmean almost periodic mild solutions to the system.

16.

THE EXISTENCE AND STABILITY OF ALMOST PERIODIC SOLUTION





Ni Hua Lin Faxing《Annals of Differential Equations》,2007年第23卷第2期


By using the ordinary dichotomy and theory of stability,we study the nonli near differential equation and obtain some sufficient conditions which guarantee the existence and stability of almost periodic solution for the nonlinear diffe rential equation.

17.

Weighted pseudo almost periodic solutions of Nth order neutral differential equations with piecewise constant arguments





Rong Kun Zhuang Rong Yuan《数学学报(英文版)》,2014年第30卷第7期


In this work, we present some existence theorems of weighted pseudo almost periodic solutions for Nth order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.

18.

THE EXISTENCE AND UNIQUENESS OF ALMOST PERIODIC SOLUTION OF x"+cx'+g(x)=P(t,x)





林木仁《Annals of Differential Equations》,2002年第3期


This paper studies equation x" + cx' + g(x) = P(t,x). Under some suitable conditions the existence and uniqueness of almost periodic solution of this equation are given.

19.

SEMILINEAR SYSTEMS OF BACKWARD STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN R~n





TANG Shanjian《数学年刊B辑(英文版)》,2005年第26卷第3期


This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semilinear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs. The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.

20.

ALMOST PERIODIC SOLUTIONS TO SOME NONLINEAR DELAY DIFFERENTIAL EQUATION





《Annals of Differential Equations》,2009年第4期


The existence of an almost periodic solutions to a nonlinear delay diffierential equation is considered in this paper. A set of sufficient conditions for the existence and uniqueness of almost periodic solutions to some delay diffierential equations is obtained.
