一致最终有界性与无限时滞泛函微分方程周期解

本文证明了在具有衰减记忆的允许相空间中,无限时滞泛函微分方程的解的一致最终有界性蕴含了周期解的存在性．     

无限时滞中立型随机泛函微分方程解的存在唯一性

有限时滞随机泛函微分方程的存在唯一性已经得到较多的研究,但对于无限时滞随机泛函微分方程的性质极少.本文在不需要线性增长条件,在一致Lipschitz条件下证明了无限时滞中立型随机泛函微分方程的存在唯一性,给出了精确解和近似解的误差估计,最后给出了解的矩估计.     

无限时滞线性中立型泛函微分方程周期解 (英)

本文以Cg空间为相空间,证明了具无限时滞D算子型线性中立型泛函微分方程存在周期解当且仅当存在有界解,得到了与以往结论互不包含的结果．     

泛函微分方程的全局稳定周期解

本文综合运用相空间理论，泛函分析方法和李雅普诺夫第二方法，研究具无限时滞的泛函微分方程周期解的存在性，唯一性和稳定性问题，得到了新的结果．     

无限时滞随机泛函微分方程的Razumikhin型定理

在无限时滞的随机泛函微分方程整体解存在的前提下,建立了一般衰减稳定性的Razumikhin型定理.在此基础上,基于局部Lipschitz条件和多项式增长条件,得到了无限时滞随机泛函微分方程整体解的存在唯一性,以及具有一般衰减速率的p阶矩和几乎必然渐近稳定性定理.     

带无限时滞的抽象泛函微分方程的解

本文在满足某些基本公理的抽象相空间中建立了一类带无限时滞的抽象泛函微分方程Cauchy问题解的一些存在唯一性定理及一个非线性算子半群表示定理.     

具无限时滞中立型泛函微分方程解的稳定性与有界性

以相空间为基础，研究了具有无限时滞中立型泛函微分方程解的稳定性和有界性，建立了方程解为一致稳定，一致渐近稳定的充要性判据；证明了当方程右端泛函满足Lipschitz条件时，解的一致渐近稳定性蕴涵了有界解的存在性，推广了文献［4-6］中已有的相关结果.     

关于泛函微分方程解的两个重要不等式

以 ( Cn,|· |h)空间 [2 ] 为相空间 ,研究了具有无限时滞中立型泛函微分方程 ,得到了方程解的两个重要不等式     

具有无穷时滞泛函微分方程的周期解

讨论具有无穷时滞中立型泛函微分方程的周期解问题.利用矩阵测度和Krasnoselskii不动点定理得到了周期解的存在性和唯一性定理;特别地,当Q（s）为零矩阵,A（t,x）=A（t）时给出了存在唯一稳定的周期解的条件.     

上下解方法给出具有时滞随机泛函微分方程解的存在性(英文)

讨论了具有不连续飘逸系数具有时滞的随机泛函微分方程,通过上下解方法和序拓扑空间中不动点原理给出了其解的存在性定理.     

The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay

This paper is devoted to build the existence-and-uniqueness theorem of solutions to stochastic functional differential equations with infinite delay (short for ISFDEs) at phase space BC((−∞,0];Rd). Under the uniform Lipschitz condition, the linear growth condition is weaked to obtain the moment estimate of the solution for ISFDEs. Furthermore, the existence-and-uniqueness theorem of the solution for ISFDEs is derived, and the estimate for the error between approximate solution and accurate solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence-and-uniqueness theorem is also valid for ISFDEs on [t₀,T]. Moreover, the existence-and-uniqueness theorem still holds on interval [t₀,∞), where t₀∈R is an arbitrary real number.     

一类可扩充杆横截挠度方程的Cauchy问题

讨论一类刻划可扩充杆横截挠度的非线性双曲型方程utt+A2u+M(x，‖A1/2 u ‖22)Au=0，这里A=-Δ+I，x∈R\+n，Cauchy问题解的存在唯一性，给出了此 方程有唯一局部解的存在定理.文章所给出的结果的适用性要远大于已有的与此问题相关的结论，对此方程非线性 项的假设要比一般的多.事实上，文章的结果是在打破了以前的所有限制而得到的.      

双对称非负定阵一类逆特征值问题的最小二乘解

１．引言 逆特征值问题在工程中有广泛的应用,其研究已有一些很好的结果［１－５］．最近,文［６］还研究了双对称矩阵逆特征值问题,即研究了如下两个问题： 问题Ａ．已知Ｘ∈Ｒｎｘｍ,Ａ＝ｄｉａｇ（λ１…,λｍ）,求Ａ∈ＢＳＲｎｘｎ使 ＡＸ＝ＸＡ,其中 Ｒｎｘｍ表示全体 ｎ ｘ ｍ实矩阵集合, ＢＳＲｎｘｎ表示全体 ｎ ｘ ｎ双对称阵集合． 问题Ｂ．已知Ａ＊ＥＲｎｘｎ,求Ａ∈ＳＥ使 ｜｜Ａ＊－Ａ｜｜＝ ｉｎｆ ｜｜Ａ＊－Ａ｜｜ ＡＦＳＥ其中 ＳＥ是问题 Ａ的解集合,｜｜． ｜｜表示 Ｆｒｏｂｅｎｉｕｓ范数． 在实际问题中, …     

矩阵方程AX=B的双反对称最佳逼近解

本文主要讨论下而两个问题并得到相关结果:问题Ⅰ:给定A ∈ R~(k×n),B ∈ R~(k×n),求X ∈ BASR~(n×n),使得AX=B.问题Ⅱ:给定X* ∈R~(n×n),求X使得‖X-X~*‖=minX∈S_E‖X-X~*‖,其中S_E是问题Ⅰ的解集合,‖·‖是Frobenius范数.通过对上述问题的讨论给出了问题Ⅰ解存在的充分必要条件和其解的一般表达式同时给出了问题Ⅱ的解,算法,和数值例子.     

Weighted pseudo-almost automorphic solutions for some partial functional differential equations

In this paper, we study the existence and uniqueness of a weighted pseudo-almost automorphic solution for some nonhomogeneous partial functional differential equations. We use the variation of constants formula developed in Ezzinbi and N’Guérékata (2007) [11] and the spectral decomposition of the phase space to show the main result of this work. To illustrate our main result, we study the existence and uniqueness of a weighted pseudo-almost automorphic solution for some diffusion equations with delay.     

带无限时滞中立型随机泛函微分方程的解的存在唯一性

In this paper, we will make use of a new method to study the existence and uniqueness for the solution of neutral stochastic functional differential equations with infinite delay (INSFDEs for short) in the phase space BC((?∞,0];Rd). By constructing a new iterative scheme, the existence and uniqueness for the solution of INSFDEs can be directly obtained only under uniform Lipschitz condition, linear grown condition and contractive condition. Meanwhile, the moment estimate of the solution and the estimate for the error between the approximate solution and the accurate solution can be both given. Compared with the previous results, our method is partially different from the Picard iterative method and our results can complement the earlier publications in the existing literatures.     

平均非扩张映射的公共不动点性质

研究了平均非扩张型映射T:‖Tx-Ty‖≤a‖x-y‖+b‖x-Tx‖+c‖x-Ty‖,(x,y∈K,a,b,c≥0,a+b+c≤1)的公共不动点的存在性和唯一性.得到平均非扩张型映射T1和T2满足T1T2=T2T1,则T1T2存在唯一的不动点,并且T1和T2存在唯一的公共不动点.本文结果是近期相关文献结果的推广.     

The Existence and Uniqueness of the Solution for Neutral Stochastic Functional Differential Equations with Infinite Delay in Abstract Space

The main aim of this paper is to prove the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay, which the initial data belong to the phase space ℬ((−∞,0];ℝ ^d ). The vital work of this paper is to extend the initial function space of the paper (Wei and Wang, J. Math. Anal. Appl. 331:516–531, 2007) and give some examples to show that the phase space ℬ((−∞,0];ℝ ^d ) exists. In addition, this paper builds a Banach space ℳ²((−∞,T],ℝ ^d ) with a new norm in order to discuss the existence and uniqueness of the solution for such equations with infinite delay.     

随机森林发展系统解的存在性和唯一性

本文根据Gronwall's和Barkholder-Davis-Gundy's引理，证唠了Hilbert空间的随机森林发展系统解的存在性和唯一性．     

The solution to the BCS gap equation and the second-order phase transition in superconductivity

The existence and the uniqueness of the solution to the BCS gap equation of superconductivity are established in previous papers, but the temperature dependence of the solution is not discussed. In this paper, in order to show how the solution varies with the temperature, we first give another proof of the existence and the uniqueness of the solution and point out that the unique solution belongs to a certain set. Here this set depends on the temperature T. We define another certain subset of a Banach space consisting of continuous functions of both T and x. Here, x stands for the kinetic energy of an electron minus the chemical potential. Let the solution be approximated by an element of the subset of the Banach space above. Second, we show, under this approximation, that the transition to a superconducting state is a second-order phase transition.