二阶微分方程解的零点分布

应用角域Nevanlinna理论和Ahlfors覆盖曲面理论, 研究了二阶微分方程f’’+A(z)f=0的解的零点分布. 证明了在复平面上至少存在一条半直线, 使得二阶微分方程解在该直线上的零点的径向收敛指数为无穷. 用新的方法证明了伍胜健在文献[5]中的一个定理.     

二阶微分方程解关于超级的零点分布

设f1和f2是二阶微分方程f″+A(z)f=0.的两个线性无关的解,其中A(z)是无穷级整函数且超级δ2(A)<∞.令E=f1,f2.文章研究了E的超级为无穷的Borel方向和零点聚值线之间的关系.所得结果推广并改进了文献[7]中的一个结果.     

高阶齐次线性微分方程解的零点

研究了一类高阶齐次线性微分方程解的零点收敛指数,并得到当方程的系数A_0为整函数,其泰勒展式为缺项级数,并且A_0起控制作用时,方程f~((k))+A_(k-2)f~((k-2))+…+A_1f′+A_0f=0的任意两个线性无关解f_1,f_2满足max{λ(f_1),λ(f_2)}=∞,其中λ(f)表示亚纯函数.f的零点收敛指数.     

一类二阶线性微分方程解的增长性

本文研究一类二阶齐次线性微分方程f"+A_1(z)e~(P(z))f'+A_0(z)e~(Q(z))f=0,解的增长性,其中P(z)=az~n,Q(z)=bz~n,ab≠0,a=cb(c1),A_j(z)(j=0,1)是非零多项式,证明了该方程的每个非零解满足σ(f)=∞并且σ_2(f)=n.     

二阶亚纯系数微分方程解的零点分布

应用角域Nevanlinna理论,研究了二阶亚纯系数微分方程f′′+A(z)f=0的解的零点聚值线和Borel方向之间的关系.推广了文献[5]中的一个定理.     

二阶齐次与非齐次线性微分方程亚纯解的零点与增长性质估计(英文)

本文研究了方程f′′+A(z)f′+B(z)f=0与f′′+A(z)f′+B(z)f=F亚纯解的零点与增长性,其中A(z),B(z)(■0),F(z)(■0)为亚纯函数,得到了方程亚纯解的增长级、下级、超级、二级不同零点收敛指数等的精确估计,改进了KwonKi-Ho、陈宗煊与杨重骏、Benharrat Beladi等的结果.     

Bounds for Zeros of Solutions of Second Order Differential Equations with Polynomial Coefficients

We consider the equation ${u''=P(z)u\;\;(z\in\mathbb{C})}$ where P(z) is a polynomial. Let z _k (u), k = 1, 2,... be the zeros of a solution u(z) to that equation. Bounds for the sums $$\sum_{k=1}^{j} \frac {1} {|z_k(u)|}\;(j=1, 2, \ldots)$$ are established. Some applications of these bounds are also considered.     

高阶亚纯系数非齐次线性微分方程解的零点

讨论一类高阶亚纯系数非齐次线性微分方程解的零点问题,当方程的系数A0是亚纯函数且满足δ(∞,A0)=δ(0)和lim(r→∞)log T(r,Ao)/log r=∞时,如果f1和f2是方程f((k))+A(κ—1)f((k—1))+…+Aof=F的两个线性无关解,得到max{λ(f1),λ(f2)}=∞.还考虑了σ(F)=∞或Ad(1dκ—1)满足lim(r→∞)log m(r,Ad)/log r=∞的情况.     

On Periodic Solutions of Second Order Linear Difference Equations

In this paper, we apply a new procedure initially developed in Refs. [H. El-Owaidy and H.Y. Mohamed. "On the periodic solutions for nth order difference equations". Journal of Applied Mathematics and Computation , (to appear); "The necessary and sufficient conditions of existence of periodic solutions of nonautonomous difference equations". Journal of Applied Mathematics and Computation , (to appear)] to simplify the use of Carvalho's method to the case of discrete difference equations, in order to find the periodic solutions of second order linear difference equations. We can also find the complex periodic solutions.     

二阶周期线性微分方程解的几个性质

In this paper,the zeros of solutions of periodic second order linear differential equation y ＋ Ay = 0,where A（z） = B（e z ）,B（ζ） = g（ζ） ＋ p j=1 b ？j ζ ？j ,g（ζ） is a transcendental entire function of lower order no more than 1/2,and p is an odd positive integer,are studied.It is shown that every non-trivial solution of above equation satisfies the exponent of convergence of zeros equals to infinity.     

Subnormal Solutions of Second Order Linear Differential Equations With Periodic Coefficients

We find the form of all subnormal solutions of equation (1.4). Our results generalize and improve a well-known result of Wittich about equation (1.1). Several examples are given. Higher order equations are discussed.     

On Some Second Order Differential Equations with Convergent Solutions

Via a special integral transformation, asymptotic integration results for ordinary differential equations are used to establish accurate asymptotic developments for radial solutions of the elliptic equation Δu + K(|x|)e ^u = 0, |x| > x ₀ > 0, in the bidimensional case.     

The Separation of Zeros of Solutions of Higher Order Linear Differential Equations With Entire Coefficients

Suppose that a homogeneous linear differential equation has entire coefficients of finite order and a fundamental set of solutions each having zeros with finite exponent of convergence. Upper bounds are given for the number of zeros of these solutions in small discs in a neighbourhood of infinity.     

On the Number of Zeros of Nonoscillatory Solutions to Higher-Order Linear Ordinary Differential Equations

 This paper is concerned with the problem of counting the number of zeros of bounded nonoscillatory solutions of higher-order linear ordinary differential equations involving a parameter. It is shown that a recent result for the second-order case is still valid for the higher-order case. Received September 20, 2001; in revised form February 8, 2002 Published online July 12, 2002     

On the Number of Zeros of Nonoscillatory Solutions to Higher-Order Linear Ordinary Differential Equations

 This paper is concerned with the problem of counting the number of zeros of bounded nonoscillatory solutions of higher-order linear ordinary differential equations involving a parameter. It is shown that a recent result for the second-order case is still valid for the higher-order case.     

A Note on Meromorphic Solutions of Linear Partial Differential Equations of Second Order

We will prove a uniqueness theorem for meromorphic solutions of linear partial differential equations of second order with polynomial coefficients associated with the Jacobi differential equations and their generalizations.     

Nonoscillation Characterizations of Second Order Linear Differential Equations

In this paper, we establish some nonoscillatory characterizations of solutions of the second order linear differential equation (pu′)′ + qu = 0. Using these characterizations, we give some comparison theorems improving the results of Hille , Wintner , Wong and Yu .     

2阶抽象微分方程的周期解

本文考虑Banach空间中形如x″=A(t)x f(t,x,x′)的2阶微分方程,利用基于度理论的一定不动点定理得到了以上方程存在周期解的若干充分条件。     

Common Zeros of the Solutions of Two Non-Homogeneous First Order Differential Equations

We consider two non-homogeneous first order differential equations and we use Nevanlinna theory to determine when the solutions of these differential equations can have the same zeros or nearly the same zeros.     

高阶线性微分方程的解的定性状态

本文的目的是考查高阶线性微分方程解的定性状态，建立方程分类的某些条件．我们还给出了方程解的振动判据．