半序度量空间与半序Banach空间中一类算子方程的可解性

在L,N都不必连续的情况下,利用半序方法,研究了算子方程Lx=Nx的可解性,得到了该方程在完备度量空间与Banach空间中解的存在性与多解性结果,并将所获结果应用于一个微分-积分方程的周期边值问题.     

半序空间中二元算子方程的可解性及应用

首先在Banach空间中,利用半序方法和锥理论,研究了混合单调算子方程Lx=N(x,y)在反向上下解条件下的耦合解的存在性.然后在完备度量空间和Banach空间中,利用半序方法和锥理论,研究算子方程Lx=N(x,x)解的存在性唯一性问题,得到了一些新结论.所得的部分结论改进了最近一些文献中的重要结果.最后,将所得的部分结果应用于非线性算子固有值与固有元的存在性的研究中.     

序Banach空间中算子方程的迭代求解及其应用

利用半序理论和混合单调算子技巧,研究序Ｂａｎａｃｈ空间中非线性算子方程解的存在唯一性,并给出了迭代序列收敛于解的误差估计．作为应用,讨论了序Ｂａｎａｃｈ空间中一类非线性积分方程的可解性,改进和推广了某些已知结果．     

二元非混合单调算子方程组的迭代求解

利用锥与半序理论和混合单调算子理论,讨论Banach空间中非单调二元非线性算子方程组解的存在性与唯一性,并给出了收敛于方程组解的迭代序列和误差估计。改进和推广了混合单调算子方程和一元算子方程的某些相应结果。     

列序压缩算子的不动点和Hammerstein型积分方程

给出了Banach空间列序压缩算子定义,讨论了此类算子不动点存在性问题和其在非线性H amm erste in型积分方程中的应用.     

序Banach空间中一类算子方程的可解性

利用改进的Mnch紧性条件,研究了一类算子方程Lx=Nx的解的存在性．本文结果并没有要求算子L和N的连续性．作为应用,讨论了右端项不连续的隐式椭圆偏微分方程的边值问题的解的存在性．     

一类半空间上非线性椭圆方程正解的存在性

本文考虑半空间上的方程正解的存在性,其中 通过引入带权的空间,将方程转化为在带权空间求约束极小,运用“集中紧致”原理,证明了正解的存在性。     

热方程的一些端点估计及其在Navier-Stokes方程中的应用——献给陆善镇教授75华诞

本文首先讨论热方程初值问题的解在Hardy、BMO（bounded mean oscillation）和Besov型空间中的估计.然后本文结合Coifmann-Lions-Meyer-Semmes在Hardy空间中的补偿紧性结果,给出Navier-Stokes方程整体弱解的二阶导数的一些端点估计.     

一类非线性方程的解的存在唯一性及其应用

设A是增算子或减算子,本引入广义序Lipschitz条件,不要求算子 任何紧性,连续性或凹凸性,由单调迭代技巧得到了方程Ax=x的解的存在唯一性,将所得结果应用于无界域上的Hammerstein积分方程,得到了新结果。     

一个空间和一个序空间乘积的正规性

本文讨论一个空间和一个特殊的序空间,即序数(其上带有序拓扑)乘积的正规性.所得到的结果中有些改进了已有的相应结果.例如下面的定理:定理 设 cf(α)>ω.若 t(X)相似文献   

广义Morrey空间与广义Campanato空间及其应用(Ⅰ)

Campanato空间在偏微分方程上有广泛的应用.为此本文推广了Morrey空间和Campanato空间,并研究了引入的广义Morrey空间和广义Campanato空间的性质.另文应用广义Campanato空间得到了非幂次增长椭圆偏微分方程解的正则性.     

Finite time blow up for a Navier-Stokes like equation

We consider an equation similar to the Navier-Stokes equation. We show that there is initial data that exists in every Triebel-Lizorkin or Besov space (and hence in every Lebesgue and Sobolev space), such that after a finite time, the solution is in no Triebel-Lizorkin or Besov space (and hence in no Lebesgue or Sobolev space). The purpose is to show the limitations of the so-called semigroup method for the Navier-Stokes equation. We also consider the possibility of existence of solutions with initial data in the Besov space . We give initial data in this space for which there is no reasonable solution for the Navier-Stokes like equation.

     

A space decomposition method for parabolic equations

A convergence proof is given for an abstract parabolic equation using general space decomposition techniques. The space decomposition technique may be a domain decomposition method, a multilevel method, or a multigrid method. It is shown that if the Euler or Crank–Nicolson scheme is used for the parabolic equation, then by suitably choosing the space decomposition, only O(| log τ |) steps of iteration at each time level are needed, where τ is the time-step size. Applications to overlapping domain decomposition and to a two-level method are given for a second-order parabolic equation. The analysis shows that only a one-element overlap is needed. Discussions about iterative and noniterative methods for parabolic equations are presented. A method that combines the two approaches and utilizes some of the good properties of the two approaches is tested numerically. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 27–46, 1998     

A Newton-like method and its application

In this paper we prove an existence and uniqueness theorem for solving the operator equation F(x)+G(x)=0, where F is a Gateaux differentiable continuous operator while the operator G satisfies a Lipschitz-condition on an open convex subset of a Banach space. As corollaries, a theorem of Tapia on a weak Newton's method and the classical convergence theorem for modified Newton-iterates are deduced. An existence theorem for a generalized Euler-Lagrange equation in the setting of Sobolev space is obtained as a consequence of the main theorem. We also obtain a class of Gateaux differentiable operators which are nowhere Frechet differentiable. Illustrative examples are also provided.     

NUMERICAL SOLUTION OF THE SPACE FRACTIONAL DIFFERENTIAL EQUATION

In this paper, a space fractional differential equation is considered. The equation is obtained from the parabolic equation containing advection, diffusion and reaction terms by replacing the second order derivative in space by a fractional derivative in space of order. An implicit finite difference approximation for this equation is presented. The stability and convergence of the finite difference approximation are proved. A fractional-order method of lines is also presented. Finally, some numerical results are given.     

A new method to solve the damped nonlinear Klein-Gordon equation

This paper discusses a damped nonlinear Klein-Gordon equation in the reproducing kernel space and provides a new method for solving the damped nonlinear Klein-Gordon equation based on the reproducing kernel space.Two numerical examples are given for illustrating the feasibility and accuracy of the method.     

A fixed point theorem and its application to integral equations in modular function spaces

In this paper we present a fixed point theorem of Banach type in modular space. We give an application of this result to a nonlinear integral equation in Musielak-Orlicz space.

     

The Cauchy Problem for Certain Inhomogeneous Difference-Differential Parabolic Equations

We prove an existence and uniqueness theorem for classical solutions of the Cauchy problem for an inhomogeneous equation of parabolic type with shifted space variables.     

双曲空间中Laplace-Beltrami方程的一个带位移的边值问题

讨论了双曲空间中Laplace-Beltrami方程的一个带位移的边值问题.首先将双曲空间中的Laplace-Beltrami方程的解转化为Clifford分析中的超正则函数.然后给出了超正则函数的Plemelj公式并讨论了相关奇异积分算子的性质,最后利用积分方程的方法和压缩不动点原理证明了Laplace-Beltrami方程的一个带位移的边值问题的解的存在性和唯一性.