Hilbert空间中双曲型随机线性发展方程的显示解(英文)

本文研究了Hilbert空间中的双曲型随机线性发展方程 ,证明了 ,在某些条件下得到了用“样本广义解方法”得到这类方程的显示解 ,并利用显示解证明了解的存在性与唯一性 .     

Banach空间中的半线性发展方程

讨论了Banach空间X中带有非局部条件的半线性发展方程．在g失去紧性的条件下，利用L^p（I；X）空间中的不动点定理，对边值问题适度解的存在性做了研究，完善和推广了已有结论．最后给出一个在偏微分方程中的例子．     

Banach值随机微分方程解的存在唯一性

本文我们用逐次逼近的方法研究Banach值随机微分方程解的存在性和轨道唯一性.     

On Approximation of Solutions to One Class of Stochastic Equations

Siberian Mathematical Journal -     

On Bounded Solutions of Some Classes of Two-Parameter Difference Equations in a Banach Space

We obtain criteria for the existence of bounded solutions of some classes of linear two-parameter difference equations with operator coefficients in a Banach space.     

Banach空间一类非线性积分微分方程解的存在性

本文利用Ｍ?ｎｃｈ不动点定理研究了Ｅａｎａｃｈ空间中一类非线性积分微分方程解的存在性,给出的结论改进、推广了［１－２］中的结果．     

Nonlocal Integrated Solutions for a Class of Abstract Evolution Equations

We give an introduction to the theory and to some applications of eigenvectors of tensors (in other words, invariant one-dimensional subspaces of homogeneous polynomial maps), including a review of some concepts that are useful for their discussion. The intent is to give practitioners an overview of fundamental notions, results and techniques.

     

On the Cowen-Douglas Class for Banach Space Operators

In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class if and only if T is unitarily equivalent with the operator M _z on a Hilbert space -valued analytic functions, where M _z denotes the operator of multiplication by the independent variable. The proof involves holomorphic vector bundles and Grauert’s theorem. In this paper we use a theorem by I. Gohberg and L. Rodman [4] to give a more elementary proof of this fact, which also works for Banach space operators.      

Banach空间半线性发展方程的周期解

把上、下解方法引入到有序Ｂａｎａｃｈ空间中的半线性发展方程周期解问题，利用正算子半群特征与单调迭代程序，获得了最大周期解与最小周期解的存在性．所得的结果概括和推广了常微分方程与偏微分方程中的有关结论     

Banach空间一类非线性微分积分方程的整体解

该文研究 Banach空间中一类非线性 Volterra型微分积分方程在无穷区间 R 上的耦合最小最大拟解及解的整体存在性 .利用单调迭代方法及 Monch不动点定理 ,给出了该类方程耦合最小最大拟解及解的整体存在性定理 ,改进、推广了 [1 - 2 ]中的相应结果     

有序Banach空间中一类算子方程的正解

本文考虑有序Ｂａｎａｃｈ空间中形如：ｘ＝ｙ＋Ｋｆ（·，Ｐ_１ｘ，…，Ｐ_ｎｘ）的算子方程，利用一定的不动点定理，得到了这类方程存在正解的某些充分条件。     

Extremal Solutions of a Class of Nonlinear Integro-Differential Equations in Banach spaces

The monotone iterative technique is applied to a class of nonlinear first order integro-differential equations in Banach spaces. First a linear system with a ``small' nonlinear perturbation is solved using Banach's Contraction Principle and the technique of Green's function. Then based upon a comparison result, the existence of minimal and maximal solutions is proved.

     

一类泛函方程的连续解

本文考虑泛函方程x（x（t））＋f（x（t）-t）=0，在f满足一定单调性的条件下讨论了此方程连续解的性质、解的存在性和延拓性．其结果对于求解相应的泛函微分方程具有直接的应用．     

一类非线性分数阶发展方程的新精确解

利用exp(-Φ(ξ)展开法,分别得到非线性分数阶Phi-4方程,非线性分数阶foam drainage方程,非线性分数阶SRLW方程的新精确解.实践证明,方法简洁方便,对于研究非线性分数阶发展方程具有十分重要的意义.     

复Banach空间中C-R方程的全纯解

二重复数是复数的一种推广，在其上的全纯映照族对应于Ｃ２上满足复Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的全纯映照族．可以证明，这样的映照族本质上是由二个单复变数的全纯函数的直乘积所组成的族．本文证明：即使在Ｂａｎａｃｈ空间中，Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的全纯解，具有同样的性质．     

Banach 空间一类奇异脉冲微分方程的多解存在性

该文利用不动点指数理论讨论了Banach空间中一类带奇异性的脉冲微分方程Neumann边值问题多解的存在性,并给出了应用     

On Discretization Schemes for Stochastic Evolution Equations

Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved. Mathematics Subject Classifications (2000) Primary: 60H15; Secondary: 65M60.István Gyöngy: This paper was written while the first named author was visiting the University of Paris X. The research of this author is partially supported by EU Network HARP.Annie Millet: The research of the second named author is partially supported by the research project BMF2003-01345.     

Banach空间非线性发展方程的耦合周期解

本文利用上下解方法与正算子半群理论,讨论了Banach空间中具有混合单调（混拟单调）性质的非线性发展方程耦合周期解的存在性及周期解的存在唯一性,所得结果概括并推广了有关常微分方程和偏微分方程的若干结论．