一类中立型泛函微分方程周期解的存在性

利用不动点定理研究一类中立型泛函微分方程周期解的存在性,所得结果推广了文[1]、[2]的有关结论.     

一类带有时间混合效应的泛函微分方程解的存在性

讨论了一类非线性泛函微分方程解的存在问题.通过将方程(*)关于初值x1(0)=u1,x2(0)=u2的解的存在性问题转化为讨论一个映象的不动点问题,用所得结论推广了文[6],[7]中相应的定理.     

多值微分系统及动态规划中的泛函方程的可解性

本文利用不动点定理获得了完备距离空间中多值微分方程的非线性过值问题的解的存在性定理,同时给出了动态规划中的一类泛函方程的解存在性的充分条件。     

板模型部分反射边界条件下的参数问题

本文讨论迁移理论中一类Ronen方程的可解性问题.从1976年Ronen等人提出此问题以来,关于这个方程已有许多逼近计算和数值结果,可是仅在文献[2,3]中,这个问题被严格地讨论.主要困难在于如何处理积分核。在板模型、部分反射边界下,本文利用泛函分析的方法讨论这个问题,我们得出了使迁移系统有非零解的参数的分布,推出了控制临界本征值存在的充要条件,并给出了它的存在范围。     

一类高维非自治系统的周期解

本文讨论了一类高维非自治系统的周期解的存在性问题，推广了文[1]中的一个结果.     

一类非线性抛物型方程整体解的存在性和衰减估计

本文讨论了一类拟线性抛物型方程初边值问题整体解的存在性和衰减性估计.所得结果改进并推广了文献[1],[3]和[7]的相应结果.     

共振情形下四点泛函边值问题解的存在性

运用Mawhin重合度理论,讨论了一类二阶四点泛函边值问题解的存在性和多解性.分别在非线性项f有界和无界的条件下,获得了此类泛函边值问题解的存在性结果.     

具有偏差变元的二阶泛函微分方程周期解的存在性

该文利用k- 集压缩算子抽象连续性定理和一些分析技巧研究了一类具有偏差变元的二阶泛函微分方程周期解的存在性. 该文的结果推广和改进了文献[1-2]的主要结果.     

一类拟线性退缩抛物型方程整体解的存在性与衰减估计

本文讨论了一类拟线性抛物型方程初边值问题整体解的存在性和衰减估计.所得结果改进并推广了文献[1]的相应结果.     

具有无限时滞的随机泛函微分方程的解的唯一存在性

本文主要证明了在相空间（B）中具有无限时滞随机泛函微分方程解的唯一存在性.推广了文献[2]中的相空间,并且给出了一些相空间存在的例子.另外,本文建立了一个Banach空间（M）^2t0（（-∞,T],Rd）依范数‖·‖,并在这个空间上讨论了具有无限时滞随机泛函微分方程的解的唯一存在性.     

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATIONS

The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an appplication, we utilize the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equations. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of.     

Existence and regularity of solutions for neutral partial functional integrodifferential equations with infinite delay

This paper is concerned with the existence and regularity of solutions for a class of neutral partial functional integrodifferential equations with infinite delay in Banach spaces. We use the theory of resolvent operator developed in R. Grimmer (1982) [29] to show the existence of mild solutions. We give sufficient conditions ensuring the existence of strict solutions. The phase space is axiomatically defined. Our results are applied to prove the existence and regularity of solutions to a Lotka–Volterra model with diffusion.     

Some new basic results for singularly perturbed ordinary differential equations

Asymptotic results are obtained for an initial-value problem for singularly perturbed systems. Existence of bounded solutions to singularly perturbed systems is deduced from the results of a previous paper [9]. These results significantly enlarge the class of limiting asymptotic solutions of singularly perturbed systems inasmuch as the limiting solutions satisfy equations more general than the classical reduced system. These results generalize those of Tikhonov [3] for the initial value problem, Flatto and Levinson [6] for the existence of periodic solutions and Hale and Seifert [7] for the existence of almost-periodic solutions.     

Existence of multiple positive periodic solutions for nonlinear functional difference equations

In this paper, we investigate the existence of multiple positive periodic solutions to a class of functional difference equations. We answer the open problems proposed by Y. Raffoul in [Electron. J. Differential Equations 55 (2002) 1-8] and the conditions obtained improve some recent results established there.     

一类四阶次线性奇异边值问题的正解

本文利用极大值原理和通过构造上下解给出了一类四阶次线性微分方程的奇异边值问题有C2[0,1]和C3[0,1]正解存在的充分必要条件.     

一种几何指标理论在泛函微分方程中的应用

本文给出一种Ｚｐ群作用下不变的新几何指标,利用这种指标理论,得到一 类周期时变泛函微分方程次调和解的存在性条件．同时我们对文［１］有关Ｈａｍｉｌｔｏｎ系 统次调和解存在性的猜想给出了一个新解答．     

高阶非线性中立型方程正解的渐近性及存在性

本文利用非线性分析中半序方法和增算子不动点定理，对高阶非线性中立型方程正解的渐近性进行了详细分类，并且给出了各种类型正解存在的充要条件和具体例子．     

Existence of positive pseudo almost periodic solutions to a class of neutral integral equations

In this work, a new fixed point theorem in partially ordered Banach spaces is established, and then used to prove the existence of positive pseudo almost periodic solutions to a class of neutral integral equations. Our existence theorem extends some recent results due to [E. Ait Dads, P. Cieutat, L. Lhachimi, Positive pseudo almost periodic solutions for some nonlinear infinite delay integral equations, Mathematical and Computer Modelling 49 (2009) 721–739] to a more general class of integral equations.     

Regularity properties of a class of hybrid methods

IntroductionIt is important that the discrete dynamical system given by a numerical method appliedto a continuous dynamical system can have the same dynamical properties as the underlyingcontinuous system. Recently, many authors[1--71 have investigated the conditions under whichspurious solutions are not introduced by time discretization, and many interesting results aboutRunge-Kutta methods, linear multistep methods and general linear methods applied to dynamical systems of ordinary different…     

Weakly localized states for nonlinear Dirac equations

We prove the existence of infinitely many non square-integrable stationary solutions for a family of massless Dirac equations in 2D. They appear as effective equations in two dimensional honeycomb structures. We give a direct existence proof thanks to a particular radial ansatz, which also allows to provide the exact asymptotic behavior of spinor components. Moreover, those solutions admit a variational characterization as least action critical points of a suitable action functional. We also indicate how the content of the present paper allows to extend our previous results for the massive case [5] to more general nonlinearities.