Existence of Single and Multiple PositivePeriodic Solutions for a Kindof Delay Logistic Equations

W匕eonsider the existenee of single and multiple positive periodie solutions for the generalperiodie Logistie equation ,‘(t)=夕(t)!a(t)一f(t,夕(t一几(t)),…,夕(t一几,(t)))],t‘R,(E)wheref:Rx皿+’‘什矿15 eontinuous,a(t)〔C(皿,R+),瑞(亡)〔C(R,R),anda(t)=a(t+T),几二(t)=爪(t+T),饥=1,…,,z,f(t,。1,。2,…,。,,)=f(亡+T,。,,。2,…,。。),T>O· It 15 well known that many matliematieal eeologieal Logistie equations are related to tl、eequation(E),e.g.,(1)the single speeies periodie populatio,i ,,…     

On the Nonexistence of Laurent Polynomial First Integrals for General Semi－quasihomogeneous Systems

An autonomous system of ODFs which admitting a quasi-homogeneous group of symmetries is called a quasihomogeneous one.     

具有相交性质的近小扭转映射的不变环面的保持性

In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will survive afer small perturtations. The persisted invariant tori are close to the unperturbed ones when the perturbation are small. The orbits reduced by those mappings are quasi-periodic in the invariant tori with the frequences closing to the original ones.     

二阶非线性微分方程的斜周期边值问题

In this paper a uniqueness theorem for a skewperiodic boundary value problem is obtained. By using the optimal control method, we derive the best estimate for the integration mean ensuring that the results hold.     

泛函微分方程周期解的非回复性定理

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

求常微分方程周期解的同伦方法

As an important aspect of applications, it is discussed how to find periodic solutions for ordinary differential equations. By using the homotopy method, a global method for finding those solutions is proposed.     

偶数阶微分方程的两点边值问题

利用对称双线性型引理和Schauder不动点定理,本文对一类偶数阶非线性微分方程给出存在唯一性定理.     

优化方法解决无上层约束的线性双层规划问题

In this paper we propose an optimal method for solving the linear bilevel programming problem with no upper-level constraint. The main idea of this method is that the initial point which is in the feasible region goes forward along the optimal direction firstly. When the iterative point reaches the boundary of the feasible region, it can continue to go forward along the suboptimal direction. The iteration is terminated until the iterative point cannot go forward along the suboptimal direction and effective direction, and the new iterative point is the solution of the lower-level programming. An algorithm which bases on the main idea above is presented and the solution obtained via this algorithm is proved to be optimal solution to the bilevel programming problem. This optimal method is effective for solving the linear bilevel programming problem.     

LaSalle''''s Theorem for Stochastic Differential Equations

In this paper, we establish a the LaSalle's theorem for stochastic differential equation based on Li's work, and give a more general Lyapunov function which it is more easy to apply. Our work has partly generalized Mao's work.     

偶数阶微分方程的两点边值问题

利用对称双线性型引理和Ｓｃｈａｕｄｅｒ不动点定理,本文对一类偶数阶非线性微分方程给出存在唯一性定理．