时滞Lokta-Volterra生态模型的同伦分析解法

研究了时滞Lolta-Volterra生态模型.利用同伦分析方法,得到了该模型解的近似展开式,并对近似解与数值解进行了比较.比较结果表明,近似解具有较高的精度,该方法用于生态模型研究可行.     

含有时滞的CES生产函数的资产投资模型解的稳定性

研究含有非局部和时滞边界条件的投资控制模型在解的存在唯一性基础上,讨论了模型解的稳定性,得到解的渐进稳定性.     

带磁场的广义Zakharov模型的奇异解

该文研究了带磁场的广义Zakharov模型的奇异解.得到了带磁场的广义Zakharov模型奇异解存在的充分条件,以及奇异解的下界速率.     

Lotka-Volterra模型全局指数稳定性和相应方程解的分岔

研究具有变系数的时滞Lottka-Volterra模型,证明该模型在适当的条件下存在正的平衡解,并给出了正平衡解指数稳定的充分条件,进一步讨论了模型(1)的相对退化形式的解产生Hopf分岔现象.     

一类海-气振子ENSO模型的同伦分析解法

研究了一个ENSO海-气时滞振子模型.利用同伦分析方法,得到了该模型解的近似展开式,通过与特殊情况下的精确解比较,得到的二级近似解具有较高的精度.     

一个供应链系统可靠性模型时间依赖解的渐近行为

本文研究一个供应链系统可靠性模型的时间依赖解.利用C0-半群理论研究该模型相应算子的谱的特征,获得了该系统模型时间依赖解的渐近行为,推广了文献[8]中的结果.     

一类生物捕食模型解的整体存在性和爆破性

研究了一类具有捕食速率的生物捕食模型解整体存在性和爆破性,利用反映扩散方程组的比较原理,通过构造自相似形式的上下解,得到了模型的解的整体存在和爆破条件.     

一类两相模型的导数估计

将一类两相模型作了一个推广．将模型中的Laplace算子换成P—Laplace算子后,研究了方程的解,得出解的一个导数估计．     

一类经典趋化性模型行波解的存在性

该文研究了一类经典趋化性模型Keller-Segel模型行波解的存在性.对Keller-Segel模型中的抛物-抛物型偏微分方程组和抛物型方程,该文研究了它们正行波解的存在性和波速.     

一具有外源和内部感染的捕食-食饵模型的定性分析

研究了一类具有外源和内部感染的捕食-食饵模型在Neumann边界条件下的共存态问题.首先利用特征值理论证明了该模型正常数平衡解的渐近稳定性;然后,给出了正平衡解的先验估计;最后利用度理论研究了非常数正平衡解的存在性.     

Fej\''{e}r type inequalities for Harmonically-convex functions with applications

In this paper, a new weighted identity involving harmonically symmetric functions and differentiable functions is established. By using the notion of harmonic symmetricity, harmonic convexity and some auxiliary results, some new Fej\''{e}r type integral inequalities are presented. Applications to special means of positive real numbers are given as well.     

带有加权Hardy-Sobolev临界指数的非齐次Neumann边界奇异的多解问题

主要研究了非齐次Neumann边界奇异的问题,利用Ekeland变分原理、山路引理和一些分析技巧,证明了正解的存在性.     

Integral representation and asymptotic behavior of harmonic functions in half space

Using Carleman's formula of a harmonic function in the half space and Nevanlinna's representation of a harmonic function in the half sphere, we prove that a harmonic function, whose positive part satisfies a slowly growing condition, can be represented by a certain integral. This improves some classical Poisson integrals for harmonic functions.     

Dependence of stability of Nicholson''s blowflies equation with maturation stage on parameters

The stability of Nicholson''s blowflies equation with maturation stage is investigated by reducing the number of parameters in the original model. We derive the condition on the stability of the positive equilibrium of the model, and discuss the dependence of the stability on the parameters by analyzing geometrically the dependence of real parts of eigenvalues of the characteristic equation with fewer parameters on the parameters. By restoring parameters, the condition on the stability of the positive equilibrium of the original model are formulated explicitly, and the corresponding regions are depicted for some different cases. The obtained result shows that the parameter determining the maximum reproductive success of the population affects only the size of the positive equilibrium, but plays no role in determining its stability.     

受L\''evy噪声扰动的Logistic方程的全局吸引性

本文考虑了受L\''evy噪声扰动的Logistic方程. 在合适的条件下, 我们得到了解的全局存在性与唯一性; 我们证明了当初始值小于环境的容纳量时, 唯一的正的平衡态具有全局吸引性.     

Existence of positive periodic solution for variable–coefficient third‐order differential equation with singularity

In this paper, we investigate a class of singular third‐order differential equations with variable coefficients. By application of Green's functions and Schauder's fixed point theorem, sufficient conditions for the existence of positive periodic solutions are established. Copyright © 2013 John Wiley & Sons, Ltd.     

带阻尼项的二阶奇异耦合系统的正周期解

We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′+ p_1(t)x′+ q_1(t)x = f_1(t, y(t)) + c_1(t),y′′+ p_2(t)y′+ q_2(t)y = f_2(t, x(t)) + c_2(t),where pi, qi, ci ∈ C(R/T Z; R), i = 1, 2; f_1, f_2 ∈ C(R/T Z ×(0, ∞), R) and may be singular near the zero. The proof relies on Schauder's fixed point theorem and anti-maximum principle.Our main results generalize and improve those available in the literature.     

指数Diophantine方程4~x+b~y=(b+4)~2

本文研究了指数Diophantine方程4~x+b~y=(b+4)~2的解.设b1是给定的正奇数,运用有关指数Diophantine方程的已知结果以及有关Pell方程的Stormer定理的推广,证明了方程4~x+b~y=(b+4)~2仅有正整数解(x,y,z)=(1,1,1).     

Norm inequalities for the spectral spread of Hermitian operators

In this work, we introduce a new measure for the dispersion of the spectral scale of a Hermitian (self-adjoint) operator acting on a separable infinite-dimensional Hilbert space that we call spectral spread. Then, we obtain some submajorization inequalities involving the spectral spread of self-adjoint operators, that are related to Tao's inequalities for anti-diagonal blocks of positive operators, Kittaneh's commutator inequalities for positive operators and also related to the arithmetic–geometric mean inequality. In turn, these submajorization relations imply inequalities for unitarily invariant norms (in the compact case).     

Asymptotic Behavior of a Stochastic Predator-prey Model with Beddington-DeAngelis Functional Response and L\''{e}vy Jumps

A stochastic two-prey-one-predator model with Beddington-DeAngelis functional response and L\''{e}vy jumps is proposed and investigated in this paper. First of all, we prove the existence and uniqueness of the global positive solution, and stochastic ultimate boundedness of the solution. Next, under a simple assumption, by using It\^{o} formula and other important inequalities, some sufficient conditions are established to ensure the extinction and persistence in the mean of the system. The results show that neither strong white noise nor L\''{e}vy noise is conducive to the persistence of the population. Finally, the theoretical results are verified by numerical simulations.