带有第三边值的捕食模型的正稳态解的存在性

本文研究了一个捕食者带有第三类边界条件、被捕食者带有Neumann边界条件的捕食模型．获得了捕食模型正稳态解的存在性和非存在性结果．并且,证明了它的正稳态解的局部稳定性和唯一性．     

被捕食者带有第三边值的捕食模型的正稳态解的存在性

该文研究了一类被捕食者带有第三边值的捕食模型. 首先获得了它存在正稳态解的充要条件是a>mb+d₁λ₁; 然后研究了它的正稳态解的局部稳定性和唯一性;最后讨论了充分大的扩散参数对它的正稳态解的存在性的影响.     

带有交叉扩散的捕食模型的非常数正稳态解的存在性

本文研究了下列带有交叉扩散的捕食模型的稳态问题的非常数正解的存在性,证明了当d4>1/m1v-u时存在(g1,d2,d3)使得稳态问题存在非常数正解;而当d4≤1/m1v-u或者d1≥m1v-u/u1或者a(m1b,a2(b))时稳态问题不存在非常数正解．     

脉冲Holling-Ⅱ型时滞捕食系统正周期解的存在性

本文研究了一类食饵有扩散的脉冲Holling-Ⅱ型时滞捕食者-食饵系统.利用重合度理论,获得了该系统至少存在一个正周期解的充分条件,从而使该种群达到了一个新的适宜各物种持续共存、发腱的稳定状态.     

一类带扩散的捕食模型非常数正解的存在性

本文考虑了一类带扩散的捕食模型的平衡态问题.首先给出了正解的先验估计,进而,分别借助于能量方法和拓扑度理论得出了因参数的变化而引起的非常数正解的不存在性和存在性结果.     

Holling-Ⅲ型食饵捕食系统的四个正周期解

通过使用一般连续理论和微分不等式技巧,研究带有收获项的Holling-Ⅲ型食饵捕食系统的动态特征,并获得带有收获项的Holling-Ⅲ型食饵捕食系统存在四个正周期解的充分条件.     

一类捕食-被捕食模型的正平衡解存在性

针对自然界中捕食者染病的现象,建立了捕食者染病的捕食-被捕食模型,研究了捕食者为躲避疾病进行扩散,并且具有HollingⅡ功能性反应函数和齐次Neumann边界条件的问题,利用Harnack不等式和最大值原理给出反应扩散问题的正平衡解的先验估计,并利用拓扑度理论证明该问题的非常数正平衡解的存在性.讨论了对应平衡态问题的非常数正平衡解存在性。     

非均匀Chemostat中非单食物链模型稳态正解的存在性

研究一类由反应扩散方程组描述的非均匀Chemostat中微生物之间既表现竞争关系又表现捕食被捕食关系的模型．用特征值理论确定了系统正稳态解存在的必要条件，用锥映射不动点指数方法给出了系统正稳态解存在的充分条件．     

带雪崩项半导体方程稳态解的存在性

考虑带雪崩项半导体方程稳态模型的混合边值问题，应用Schauder不动点定理证明了逼近解的存在性，通过一系列先验估计的获得，利用紧致性原理证明了稳态弱解的存在性．     

具有饱和项的捕食食饵系统正周期解的存在性

By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficient conditions to coexistence of periodic system are obtained.     

Existence,uniqueness and stability of positive steady states to a prey-predator diffusion system

In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semi-trivial solution to the unique positive solution of the limiting system. This work was supported by National Natural Science Foundation of China (Grant Nos. 10471022, 10771032) and Natural Science Foundation of Jiangsu Province (Grant No. BK2006088)     

一类带非单调转化率的捕食-食饵模型的全局分歧

主要研究了一类带非单调转化率的捕食-食饵模型,分别以生长率a和b为分歧参数,运用度理论和分歧理论讨论了这类模型在齐次第一边界条件下全局分歧结构．     

Existence of positive solutions for a prey-predator model with refuge and diffusion

We are concerned with a prey-predator reaction-diffusion model with monotonic functional response and specific refuge size. We discuss both existence and nonexistence of positive solutions of the model by using fixed point index theory and bifurcation theory as the main argument tools. We also discuss bifurcation solutions of which stability is established by using spectrum analysis methods. Moreover, we analyze the effects of refuge size on the dynamics of the model.     

二阶三点边值问题正解的存在性

利用不动点指数定理研究了一类二阶非线性常微分方程的三点边值问题正解的存在性问题,得到了至少存在一个或无穷多个正解的几个充分条件.     

On multiplicity and stability of positive solutions of a diffusive prey-predator model

In the paper, we consider the following diffusive prey-predator model:

     

一类无穷多点边值问题正解的存在性

研究一类二阶非线性常微分方程无穷多点边值问题正解的存在性,利用不动点指数理论得到了方程至少存在一个正解的若干充分条件.     

Positive stationary solutions for a diffusive variable-territory prey-predator model

In this paper, we present results on the existence of positive stationary solutions for a diffusive variable-territory prey-predator model in heterogeneous environment, which improve and extend those of Wang and Pang (2009). In addition, the asymptotic behavior of solutions is also analyzed.     

Existence results of positive solutions to boundary value problem for fractional differential equation

In this paper, we consider the existence, multiplicity, and nonexistence of positive solutions to some class of boundary vale problem for fractional differential equation of high order. Our analysis relies on the fixed point index.      

Existence of positive solutions for a general nonlinear eigenvalue problem

Let Ω R n be a bounded domain, H = L 2 (Ω), L : D(L) H → H be an unbounded linear operator, f ∈ C(■× R, R) and λ∈ R. The paper is concerned with the existence of positive solutions for the following nonlinear eigenvalue problem Lu = λf (x, u), u ∈ D(L), which is the general form of nonlinear eigenvalue problems for differential equations. We obtain the global structure of positive solutions, then we apply the results to some nonlinear eigenvalue problems for a second-order ordinary differential equation and a fourth-order beam equation, respectively. The discussion is based on the fixed point index theory in cones.     

一类二阶常微分方程无穷多点边值问题多个正解的存在性

研究了一类二阶非线性常微分方程无穷多点边值问题多个正解的存在性,运用不动点指数理论及Holder不等式得到了方程至少存在两个正解的若干充分条件,推广和改进了相关文献的结果.