全平面上的高斯曲率方程

本文用Ｓｃｈａｕｄｅｒ不动点定理证明了一维Ｋ≥０的解、二维Ｋ≥０的径向解的存在性，同时证明了当Ｋ≤０时，在无穷远处有不同渐近性的Ｋ所对应的极大解的渐近性，并给出了径向解的刻画，推广了前人结果．     

半导体漂移-扩散方程速度饱和情形的稳态解

考虑半导体方程稳态模型的混合边值问题，应用Schauder不动点定理证明了逼近解的存在性，通过一系列先验估计的获得，利用紧致性原理证明了稳态解的存在性。     

带雪崩项半导体方程稳态解的存在性

考虑带雪崩项半导体方程稳态模型的混合边值问题，应用Schauder不动点定理证明了逼近解的存在性，通过一系列先验估计的获得，利用紧致性原理证明了稳态弱解的存在性．     

半导体方程的周期解与平衡解

本文研究半导体方程的混合初边值同题与稳态问题。利用不动点定理证明了只要所给已知资料关于时间是周期函数,则周期解必存在。同时,还证明了相应稳态问题的可解性,特别是,证明了磁敏半导体器件数学模型平衡解的存在性。     

半导体方程的周期解与平衡解

提要本文研究半导体方程的混合初边值问题与稳态问题.利用不动点定理证明了只要所给已知资料关于时间是周期函数,则周期解必存在.同时,还证明了相应稳态问题的可解性,特别是,证明了磁敏半导体器件数学模型平衡解的存在性.     

带有第三边值的捕食模型的正稳态解的存在性

本文研究了一个捕食者带有第三类边界条件、被捕食者带有Neumann边界条件的捕食模型．获得了捕食模型正稳态解的存在性和非存在性结果．并且,证明了它的正稳态解的局部稳定性和唯一性．     

具有球对称结构的相对论欧拉方程组稳态解的存在性

对于等温气体,作者将考虑具有球对称结构的相对论欧拉方程组经典稳态解(定理1.1)和弱稳态解(定理1.2)的存在性.通过求解两个常微分方程以及比较马赫数M和1的关系,定理1.1证明了相对论欧拉方程组经典稳态解的存在性.在一个C~(2,α),α∈(0,1)稳态背景解的扰动下,定理1.2将证明高维球对称跨音速(双曲-椭圆)解的存在性.     

非牛顿流体中对称扩散的稳态解

本文研究来源于非牛顿流体等许多物理现象中产生的一类扩散方程的稳态解．这类方程一般具有退化性和奇异性．利用摄动技巧证明了具对称性的古典解的存在性，并在某种一般的条件下讨论了解的唯一性     

一类旋转磁对流系统振幅方程的双波前解的存在性和稳定性分析

研究了旋转磁对流系统的振幅方程的一类稳态解的存在性和稳定性问题,得出了振幅方程的双波前解的存在性定理及相容性条件,通过变分特征化方法证明了方程解的不稳定性.     

一维稳态量子Navier-Stokes方程组古典解的唯一性

文[9]得到了一维稳态量子Navier-Stokes方程组古典解的存在性,本文在某些条件下利用一些不等式技巧继续证明了其解的唯一性.     

An asymptotic‐induced one‐dimensional model to describe fires in tunnels II: the stationary problem

We study stationary solutions of a one‐dimensional low‐Mach‐number model derived in Gasser and Struckmeier (Math. Meth. Appl. Sci. 2002; 25 (14): 1231) to describe fire events in long tunnels. The existence of solutions of the corresponding stationary model is shown to be equivalent to the existence of solutions of an algebraic problem. Multiple solutions are shown to be possible. The relation between different formulations of the problem is analysed. Weak and special distributional solutions are considered. Finally, numerical examples of realistic tunnel data with single and multiple solutions of the stationary problem are given. Copyright © 2003 John Wiley & Sons, Ltd.     

Stability and instability of stationary solutions for sublinear parabolic equations

In the present paper, we study the initial boundary value problem of the sublinear parabolic equation. We prove the existence of solutions and investigate the stability and instability of stationary solutions. We show that a unique positive and a unique negative stationary solutions are exponentially stable and give the exact exponent. We prove that small stationary solutions are unstable. For one space dimensional autonomous equations, we elucidate the structure of stationary solutions and study the stability of all stationary solutions.     

On Non-Uniqueness of Probability Solutions to the Two-Dimensional Stationary Fokker–Planck–Kolmogorov Equation

The problem of uniqueness of probability solutions to the two-dimensional stationary Fokker–Planck–Kolmogorov equation is considered. Under broad conditions, it is proved that the existence of two different probability solutions implies the existence of an infinite set of linearly independent probability solutions.     

Global smooth solutions for a one-dimensional nonisentropic hydrodynamic model with non-constant lattice temperature

In this paper, a one-dimensional nonisentropic hydrodynamic model for semiconductors with non-constant lattice temperature is studied. The model is self-consistent in the sense that the electric field, which forms a forcing term in the momentum equation, is determined by the coupled Poisson equation. The existence and uniqueness of the corresponding stationary solutions are investigated carefully under proper conditions. Then, global existence of the smooth solutions for the Cauchy problem with initial data, which are perturbations of stationary solutions, is established. It is shown that these smooth solutions tend to the stationary solutions exponentially fast as t → ∞.      

Pullback attractors for a two-dimensional Navier-Stokes model in an infinite delay case

We prove the existence of solutions for a Navier-Stokes model in two dimensions with an external force containing infinite delay effects in the weighted space C_γ(H). Then, under additional suitable assumptions, we prove the existence and uniqueness of a stationary solution and the exponential decay of the solutions of the evolutionary problem to this stationary solution. Finally, we study the existence of pullback attractors for the dynamical system associated to the problem under more general assumptions.     

广义Tjon-Wu方程Cauchy问题强解的存在唯一性和稳态解的存在性

利用卷积的性质和schauder不动点原理等技巧,在L_(1,i)空间中证明了一类广义Tjon-Wu方程Cauchy问题强解的存在唯一性以及稳态解的存在性.     

考虑Joule-Thomson效应的稳态热敏电阻问题

证明考虑Joule-Thomson效应的稳态热敏电阻问题renormalised解的存在性。     

The Asymptotic Behaviour of the Solutions of a Degenerate Reaction-diffusion Problem

Consider in this paper the existence, uniqueness and asymptotic behaviour of the solutions of the mixed problem for a class of degenerate quasilincar parabolic equations and properties of the corresponding stationary solutions.