预解算子控制的无穷时滞分数阶微分方程解的存在性

本文研究了一类预解算子控制的具有无穷时滞的分数阶泛函微分方程.利用解析预解算子理论和不动点定理,得到了具有无穷时滞分数阶微分方程适度解的存在性,推广和改进了一些已知的结果.     

关于二阶线性周期微分方程的次正规解

研究了一类二阶周期系数线性微分方程的次正规解的存在性和形式, 以及估计了所有解的增长性, 回答了Gundersen 和 Steinbart提出的一个问题.     

一类二阶变系数线性微分方程及其解的构造方法

利用构造法构造二阶变系数线性齐次微分方程及其解,根据这种方法也能求得某些二阶变系数线性齐次微分方程的非零解,并给出了二阶变系数线性齐次微分方程存在非零解的充要条件.     

单位圆盘上二阶微分方程解的增长性

研究了数是单位圆内解析函数的常微分方程的解析性质，给出了二阶线性微分方程角的增长性与系数增长性之间的关系，并进一步得到解的表示形式。     

具有n阶转向点方程的渐近解的完全表达式

本文研究二阶线性常微分方程,使用广义Airy函数得到了方程在转向点附近形式一致有效渐近解的完全表达式。     

Fredholm积-微分方程Galerkin解的加速收敛分析

本文对一般形式的线性Fredholm积-微分方程推导出迭代Galerkin解及其导数的渐近展式，从而得到了迭代解的外推估计，同时还获得了理想的校正结果．     

一类高阶线性微分方程的次正规解

讨论了一类高阶线性微分方程F~((k))+A_(k-1)f~((k-1))+…+A_0f=0,k≥2的次正规解的存在性和形式,并估计了所有解的增长性,推广了陈宗煊的结果     

Kadomtsev-Petviashvili方程的精确解

齐次平衡法是把非线性偏微分方程转换成带约束条件的线性偏微分方程的一种很好的方法 .本文在齐次平衡法的基础上具体讨论了KP方程的精确解 ,包括孤波解 ,一般的行波解 ,有理函数解和一种新类型的解 .     

某类线性微分方程亚纯解的增长性

研究了一类亚纯函数系数的线性微分方程的解的增长性问题,得到了齐次和非齐线性微分方程亚纯解的增长级、超级、二级不同零点收敛指数的精确估计．     

几类高阶线性微分方程亚纯解的增长性

本文研究了几类亚纯函数系数的高阶线性微分方程解的增长性问题,得到了齐次和非齐次线性微分方程亚纯解增长性的精确估计.     

Existence and asymptotic properties of solutions of a real system of differential equations unresolved with respect to the derivative

A system of differential equations unresolved with respect to a derivative is studied. Sufficient conditions for the existence of solutions with singular initial data are found. The dimensionality of the set of these solutions is determined and their asymptotic properties are studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1461–1464, October, 1993.     

Bisectorial operator pencils and the problem of bounded solutions

We consider a linear differential equation unresolved with respect to the derivative. We assume that the spectrum of the corresponding pencil is contained in two sectors. We study the unique existence of a bounded solution with any bounded free term.     

Numbers of subnormal solutions for higher order periodic differential equations

In this paper, we estimate the number of subnormal solutions for higher order linear periodic differential equations, and estimate the growth of subnormal solutions and all other solutions. We also give a representation of subnormal solutions of a class of higher order linear periodic differential equations.     

ON THE GROWTH OF THE SOLUTIONS FOR 1ST KIND OF HIGHER ORDER DIFFERENTIAL EQUATIONS IN THE UNIT DISC

In this paper, we study the growth of the solutions for 1st kind of differential equations of higher order in the unit disc. We give a sufficient condition for all solutions of second order linear differential equation to be inadmissible and a sufficient condition for all solutions of higher order linear differential equation to be of infinite order.     

On meromorphic solutions of linear partial differential equations of second order

This paper is concerned with entire and meromorphic solutions of linear partial differential equations of second order with polynomial coefficients. We will characterize entire solutions for a class of partial differential equations associated with the Jacobi differential equations, and give a uniqueness theorem for their meromorphic solutions in the sense of the value distribution theory, which also applies to general linear partial differential equations of second order. The results are complemented by various examples for completeness.     

亚纯函数系数微分方程的解和小函数的关系

研究了一类亚纯函数为系数的二阶非齐次线性微分方程的解及其微分多项式和小函数的关系,并得到了这类微分方程解以及解的一阶,二阶导数与微分多项式的不动点性质.     

Sturm comparison and separation theorems for linear,second order,self-adjoint,ordinary, differential equations and for first order systems

Sturm comparison and separation theorems, for first order linear combinations of solutions of linear, second order, self-adjoint, ordinary, differential equations, are obtained as consequences of Sturm comparison and separation theorems for linear combinations of components of solutions of linear, first order systems of ordinary, differential equations.     

关于常系数非齐次线性微分方程通解的注释

给出了二、三阶常系数非齐次线性微分方程的通解的表达式,并且对于任意阶常系数非齐次线性微分方程的某些类别也给出了通解的表达式.     

脉冲中立型时滞微分方程的正解的存在性

本文证明了线性脉冲中立型微分方程 [y(t)+p(t)y(t-τ)-r(t)y(t-ρ)]′+q(t)y(t-σ)=0,t≥0,t≠t_k, y(t_k~+)-y(t_k)=b_ky(t_k),k=1,2,…正解的存在性等价于一类非脉冲中立型方程正解的存在性,应用这一结果,建立了此类线性脉冲中立型微分方程正解存在性的若干充分条件。