一类具有Beddington-DeAngelis功能反应的空气污染周期动力学模型的正周期解的存在性

利用重合度理论中的延拓定理,研究了一类具有Beddington-DeAngelis功能反应的空气污染周期动力学模型的正周期解的存在性,得到了该模型存在正周期解的充分条件.     

脉冲泛函微分方程的正周期解

运用Leray-Schauder不动点定理研究一类脉冲泛函微分方程的正周期解的存在性,获得了存在正周期解的充分条件,改进了已知文献中的结果.     

具有连续时滞和比率型功能反应的竞争系统的正周期解的存在性

本文利用重合度理论中的延拓定理讨论了具有连续时滞和比率型功能反应的非自治扩散竞争系统的正周期解的存在性,得到了正周期解存在的充分条件。     

两企业竞争与合作时标动力学模型的周期行为

研究了时标上两企业竞争与合作动力学模型的周期解的存在性.运用重合度理论中的连续性定理,得到了该模型存在正周期解的一个充分条件.     

具有三个年龄阶段的自食单种群时滞模型的周期解

利用重合度理论中的延拓定理讨论了一个具有三个成长阶段的自食单种群时滞模型正周期解的存在性,得到了保证周期解存在的充分条件.     

一类无穷时滞周期Lotka-Volterra型系统的正周期解

该文研究一类无穷时滞周期Ｌｏｔｋａ Ｖｏｌｔｅｒｒａ型系统正周期解的存在性．应用Ｓｃｈａｕｄｅｒ不动 点定理得到了一个比较一般的正周期解存在定理．文献［１,２］中的主要结果被改进和推广．     

高维时滞周期的Kolmogorov型系统的正周期解

本文应用Ｂａｎａｃｈ空间中的Ｈｏｒｎ不动点得到了高维时滞的周期Ｋｏｌｍｏｇｏｒｏｖ型生态系统的正周期解存在性定理,作为这个定理的应用,讨论了几类时滞的周期ＬｏｔｋａＶｏｌｔｅｒｒａ型系统的正周期解的存在性问题,建立了新的实用的判别准则。     

一类数学生物经济模型的周期性

利用重合度理论中的延拓定理研究了一类非自治的数学生物经济模型的正周期解的存在性，得到了保证周期解存在的充分性判据．     

一类单种群系统正周期解及其稳定性

考虑周期单种群模型 dxdt=xg( t,x)± p( t,x)的正周解及其稳定性 .证明了在一定条件下 ,系统存在全局吸引的正周期解 .给出了系统存在两个正周期解的充分条件 ,同时也给出了种群灭绝的条件 .这些结果用于 Logistic模型和 Odum模型 ,得到了被开发的周期 Logistic模型存在全局吸引的正周期解 ;被开发了的周期 Odum模型只存在两个正周期解 ,其中之一吸引初值大于一个定数的所有解 ,另一个周期解则是种群灭绝的分界线     

捕食者具有阶段结构Holling II类功能性反应的捕食模型

利用重合度理论中的延拓定理讨论了捕食者具有阶段结构Holling II类功能性反应的捕食模型的正周期解的存在性,得到了保证周期解存在的充分性条件,推广了已知的相关结果. 同时通过构造Lyapunov函数得到了保证周期解稳定性的充分性条件.     

一类奇异拟线性椭圆型方程组的可解性

研究了一类P-Laplacian方程组边值问题正径向整体解的存在性和唯一性.首先,利用隐函数定理证明了该问题的局部解的存在性与唯一性,以及解对初值的连续依赖性.最后,证明了该问题存在唯一的正径向整体解.     

正线性方程组正解的判别

本文给出了正线性方程组正解的概念，给出了正线性方程组正解的若干判别方法     

Periodic solution of a two-species competitive system with toxicant and birth pulse

In this paper, we study the existence of positive periodic solution of two-species competitive system with toxicant and birth pulse. A set of easily verifiable sufficient conditions are derived for the existence of at least one positive periodic solution of the above system by using the method of coincidence degree. Numerical simulations are also presented to illustrate the feasibility of our main results.     

A necessary and sufficient condition of existence of positive solutions for nonlinear singular differential systems

In this paper, by means of monotone iterative technique, a necessary and sufficient condition of the existence of positive solution for a class of nonlinear singular differential system is established, the results of the existence and uniqueness of the positive solution and the iterative sequence of solution are given. In the end, two classes extending boundary value differential systems are discussed and some further results are obtained.     

Dynamics of an impulsive stochastic SIR epidemic model with saturated incidence rate

In this paper, the dynamics of an impulsive stochastic SIR epidemic model with saturated incidence rate are analyzed. The existence and uniqueness of the global positive solution is proved by constructing the equivalent system without pulses. The threshold which determines the extinction and persistence of the disease is obtained. The global attraction of disease-free periodic solution is addressed. Sufficient condition for the existence of a positive periodic solution is established. These results are supported by computer simulations.     

The existence of positive solution of elliptic system by a linking theorem on product space

This paper is devoted to study the existence of nontrivial positive solution of a class of elliptic system with Dirichlet Data. By using the abstract linking theorems on product space we established in Zhao et al. (Nonlinear Anal. 49 (2002) 431) we obtain the existence of three nonnegative solutions for a class of elliptic systems and the existence of a nontrivial positive solution for the problem related to the model of competing species systems involving critical Sobolev exponents.     

Positive periodic solution for a neutral delay competitive system

In this paper we study the existence of positive periodic solutions for a class of neutral type competitive system with delay. Applying the continuation theorem of coincidence degree theory, a general criteria on the existence of positive periodic solutions are established. Some the related results are generalized and improved. It is shown that the arguments delays have no effect on the existence positive periodic solution of system.     

次线性半正微分边值系统的正解

本文证明了一类含参数$\lambda>0$的半正微分边值系统正解的存在性结果.在非线性项满足次线性条件的情况下,证明了对于充分大的$\lambda>0$,方程组至少存在一个正解.     

Positive periodic solution of two-species ratio-dependent predator–prey system with time delay in two-patch environment

In this paper, we are concerned with the existence of positive periodic solution to a class of two-species ratio-dependent predator–prey diffusion model with time delay. By using the continuation theorem of coincidence degree theory, we transform this problem into a problem of calculating the topological degree of a continuous mapping, and then some sufficient conditions of the existence of positive periodic solution is established for the system.     

Global existence and blow-up of solutions to a nonlocal evolution p-laplace system with nonlinear boundary conditions

In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.