可换四元数空间中某些双曲型方程的Riemann-Hilbert边值问题

考察了在可交换四元数空间(基元为1,i,j,k满足条件i~2=j~2=-1,ij=ji= k)中的某些双曲型方程的Riemann-Hilbert边值问题,分别在不同的情况下获得了问题的可解条件和通解.     

在可交换四元数空间中的双曲方程的特征边值问题

讨论了一阶和二阶双曲复方程的特征边值问题.对其中两种线性方程,分别在不同的情况下获得通解和可解条件.而对于拟线性的二阶双曲复方程,证明了解的存在性和唯一性.     

一类具偏差变元的脉冲积分微分方程周期边值问题

通过建立有关初值问题的脉冲微分不等式,结合单调迭代技巧,获得了具偏差变元的脉冲积分微分方程周期边值问题的最大、最小解.     

二阶退化双曲型方程的Darboux型问题

本文讨论二阶退化双曲型方程的一些边值问题.文中先给出第一Darboux问题和一般斜微商边值问题的提法和解的表示式,然后使用复分析方法证明了上述问题解的存在唯一性.     

中立型脉冲双曲型方程的振动准则

Oscillation properties of the solutions of impulsive hyperbolic equations are investigated by the method of differential inequalities.     

含连续滞量和阻尼项的非线性双曲偏微分方程组的振动性

研究了一类含连续分布滞量和阻尼项的非线性双曲型偏微分方程组运用黎卡提变换获得了该方程组在两类边值条件下解振动的充分条件.     

非线性奇摄动抛物型方程初值问题的套层解

运用了初始层函数构造了一类非线性奇摄动抛物型方程初值问题解的渐近展开式,并证明了该展开式达到任意精度的一致有效性.     

一类高阶非线性双曲型方程Cauchy问题解的爆破

本文研究一类高阶非线性双曲型方程utt-uxx+μuxxx-αuxxtt+βuxxxxtt=f(ux)x的Cauchy问题,证明问题解的存在性与唯一性,并给出解在有限时刻爆破的充分条件.     

The Relation Between the Differentiability of Solution and Lower-order Terms of the Cauchy Problem for a Class of Weakly Hyperbolic Equations with Singular Coefficients

This paper discusses a class of weakly hyperbolic equations with singular coefficients. We first set up the energy inequality, ana then discuss the wellposedness of the Cauchy problem by means ot the energy inequality, and the relation between the differentiabillty of solution and lower-order terms.     

On Quasilinear Generalized Canonical Hyperbolic Systems of First-Order Partial Differential Equations

By using the method of characteristics, we prove theorems on continuous solvability and on properties of solutions of the mixed Cauchy boundary-value problem for the generalized canonical hyperbolic system of quasilinear partial differential equations of the first order in a general connected domain in (m+ 1)-dimensions.     

On Counting the Number of Eigenvalues in the Right Half-Plane for Spectral Problems Connected with Hyperbolic Systems. II. Differential Equations

This article is an immediate continuation of [1]. Solution of the Lyapunov equation leads to a boundary value problem for the first-order hyperbolic equations in two variables with data on the boundary of the unit square. In general, the problems of this kind are not normally solvable. We prove that the boundary value problems in question possess the Fredholm property under some conditions.     

On the Decay of Solutions for Some Nonlinear Dissipative Hyperbolic Equations

In this paper we show the decay of solutions to the initial-boundary value problem for somenonlinear hyperbolic equation with a nonlinear dissipative term,by using a difference inequality.     

A Nonlocal Problem with Integral Conditions for the Quasilinear Hyperbolic Equation

In this paper, we consider a nonlocal problem with integral conditions for the quasilinear hyperbolic equation in a rectangular domain. The existence and uniqueness of the generalized solution are established.     

Banach空间中含有无穷多个跳跃点的一阶脉冲积分-微分方程的无穷边值问题

通过建立一个新的比较引理,应用上下解方法和单调迭代技术,研究了Banach空间中含有无穷多个跳跃点的一阶脉冲积分-微分方程无穷边值问题在任意闭区间上最小解和最大解的存在性.     

三类多双曲复方程组的Riemann-Hilbert边值问题

用函数论的方法研究了三类超定双曲型方程组的解,即三类多双曲复方程组在一般柱形域上的Riemann-Hilbert边值问题的提法,可解条件,解的表示,唯一性和存在性.     

On the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Singular Hyperbolic Equations

In the rectangle D = (0,

On the Correctness of the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Hyperbolic Equations

It is proved that the Dirichlet problem is correct in the characteristic rectangle D _ab = [0, a] × [0, b] for the linear hyperbolic equation

Banach空间二阶非线性脉冲积分-微分方程初值问题

该文在较宽松的条件下,利用不动点理论,得到了Banach空间中二阶非线性脉冲积分-微分方程初值问题解的存在性定理.作者去掉了脉冲项的紧性和增长性限制, 因而本质上改进和推广了某些现有的结果.     

三阶两点边值问题解的存在性与唯一性

主要考虑如下三阶两点边值问题通过对非线性项f作适当的限制,利用上下解方法,获得三阶两点边值问题解的存在性结果.特别之处是,一个截断技巧和Nagumo条件的引入和使用.同时得到了解的唯一性结果.