Existence,uniqueness, stochastic persistence and global stability of positive solutions of the logistic equation with random perturbation

This paper discusses a randomized logistic equation (1) with initial value x(0)=x₀>0, where B(t) is a standard one‐dimension Brownian motion, and θ∈(0, 0.5). We show that the positive solution of the stochastic differential equation does not explode at any finite time under certain conditions. In addition, we study the existence, uniqueness, boundedness, stochastic persistence and global stability of the positive solution. Copyright © 2006 John Wiley & Sons, Ltd.     

On the global attractivity for a logistic equation with piecewise constant arguments

In this paper, we consider the following logistic equation with piecewise constant arguments:

     

Global attractivity and positive almost periodic solution for delay logistic differential equation

In this paper, we establish some sufficient conditions for the global attractivity of positive solutions and the unique existence of positive almost periodic solutions for delay logistic differential equations of the form

x^′(t)=r(t)x(t)(a(t)−b(t)x(t)−L(_xt)).$x^{\prime }\left(t\right)=r\left(t\right)x\left(t\right)(a\left(t\right)-b\left(t\right)x\left(t\right)-L\left(x_t\right))\text{.}$

Existence and global attractivity of a positive periodic solution of a class of delay differential equation

The existence and the global attractivity of a positive periodic solution of the delay differential equationy(t)=y(t) F[t, y](t-τ ₁ (t)),⋯,y(t−τ _n (t))] are studied by using some techniques of the Mawhin coincidence degree theory and the constructing suitable Liapunov functionals. When these results are applied to some special delay bio-mathematics models, some new results are obtained, and many known results are improved. Project partially supported by the National Natural Science Foundation of China (Grant No. 10572057) and the Applied Basic Research Foundation of Yunnan Province.     

广义Tjon-Wu方程Cauchy问题强解的存在唯一性和稳态解的存在性

利用卷积的性质和schauder不动点原理等技巧,在L_(1,i)空间中证明了一类广义Tjon-Wu方程Cauchy问题强解的存在唯一性以及稳态解的存在性.     

Existence and uniqueness of solutions for singular integral equation

Using the mixed monotone method we establish existence and uniqueness results for a singular integral equation. The theorem obtained is very general and complements previous known results. The work was supported by the National Natural Science Foundation of China (No.10571021 and No.10701020) and Key Laboratory for Applied Statistics of MOE(KLAS) and Subject Foundation of Harbin University (No. HXK200714).     

Existence and uniqueness of positive solutions of semilinear elliptic equations

This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to problems is given.We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear 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.     

Existence and uniqueness of solutions for a fractional differential equation with multi-point boundary value problems

In this paper, we study the existence and uniqueness solutions of a fractional differential equation with multi-point boundary value problems. By using the fixed point theorems, some new results are established and two examples are given to demonstrate the application of main results.     

EXISTENCE，UNIQUENESS AND PROPERTIES OF THE SOLUTIONS OF A DEGENERATE PARABOLIC EQUATION WITH DIFFUSION－ADVECTION－ABSORPTION

ＥＸＩＳＴＥＮＣＥ，ＵＮＩＱＵＥＮＥＳＳＡＮＤＰＲＯＰＥＲＴＩＥＳＯＦＴＨＥＳＯＬＵＴＩＯＮＳＯＦＡＤＥＧＥＮＥＲＡＴＥＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＷＩＴＨＤＩＦＦＵＳＩＯＮ－ＡＤＶＥＣＴＩＯＮ－ＡＢＳＯＲＰＴＩＯＮ￥ＳＯＮＧＢＩＮＨＥＮＧ（宋...     

Existence and global attractivity of unique positive almost periodic solution for a model of hematopoiesis

Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.     

Hopfield神经网络的周期解存在性及其全局吸引性

利用重合度理论和微分不等式分析等技巧，给出了Hopfield神经网络周期解存在性及其全局吸引性的判别准则。     

Existence and global attractivity of periodic solution for an impulsive delay differential equation with Allee effect

Sufficient conditions are obtained for the existence and global attractivity of positive periodic solution of an impulsive delay differential equation with Allee effect. The results of this paper improve and generalize noticeably the known theorems in the literature.     

Existence and global attractivity of positive periodic solutions of functional differential equations with feedback control

Sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with feedback control

The method involves the application of Krasnoselskii's fixed point theorem and estimates of uniform upper and lower bounds of solutions. When these results are applied to some special delay population models with multiple delays, some new results are obtained and some known results are generalized.     

Existence and global attractivity of positive periodic solution for an impulsive Lasota-Wazewska model

Sufficient conditions are obtained for the existence and global attractivity of periodic positive solution of an impulsive Lasota-Wazewska model for the survival of red blood cells.     

Existence and uniqueness of positive solutions for a class of semilinear elliptic systems

The authors prove the uniqueness and existence of positive solutions for the semilinear elliptic system which involves nonlinearities with sublinear growth conditions.     

一类非局部Cahn-Hilliard方程弱解的存在唯一性

研究一类对流非局部Cahn-Hilliard方程的Neumann问题.通过一致Schauder估计和Leray-Schauder不动点定理,得到了该问题经典解的存在唯一性.进而,利用弱收敛方法得到了该问题弱解的存在唯一性.     

Existence and uniqueness of solutions to a class of singular diffusion problems

Existence, uniqueness, and non-uniqueness results are given for a class of singular diffusion problems with variable diffusion rates. Continuity arguments are used on related initial value problems to produce the existence results. Uniqueness criteria are established for different sets of hypotheses and non-uniqueness results are discussed when these hypotheses fail.