一类高阶齐次线性微分方程解的零点

本文研究一类整函数系数高阶齐次线性微分方程解的零点分布.利用Nevanlinna值分布理论,得到当系数A_(k-1)的增长性起主要支配作用时,方程f~((k))+A_(k-1)f~((k-1))+···+A_0f=0任意超越解的零点收敛指数为无穷,推广了Langley和Bank等人的结果.     

一类高阶线性微分方程解的增长性

研究整函数系数高阶线性微分方程f~((k))+A_(k-1)f~((k-1))+…+A_0f=0解的增长性.利用亚纯函数的Nevanlina值分布理论,得到当系数A_s(s≠0)为满足杨不等式极端情况的整函数,A_0满足一定条件时,上述方程的每个非零解均为无穷级,并给出解的超级估计.     

一类高阶非齐次线性微分方程亚纯解的零点

利用亚纯函数的值分布理论研究了下列高阶线性微分方程解的增长性及解的零点增长性,f^((k))+A_(k-1)f((k))+A_(k-1)f^((k-1))+…+A_1f′+A_0f=F(z)其中A_0,A_1,…,A_(k-1),F≠0是亚纯函数.证明了如果A_0以∞为亏值或Borel例外值,那么方程的所有非零解的零点收敛指数均为无穷,至多除去一个例外解,获得的结果推广了以前一些文献的结论.     

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.     

无限级整函数在角域内的取值和增长性

借助熊庆来的无限级,将Nevanlinna建立的有限级整函数在角域内的取值和增长性的结果推广到无限级.作为应用,研究了高阶超越整函数系数微分方程f~((k))+A_k-2(z)f~((k-2))+…+A_1(x)f'+A_0(z)f=0解的径向振荡.     

一类高阶复微分方程解的增长性

本文研究高阶线性微分方程f~((k))+A_(k-1)f~((k-1))+···+A1f′+A0f=0解的增长性,其中Aj(j=0,···,k-1)为整函数.当存在某个系数A_s是方程ω′′+P(z)ω=0的一个非零解时,我们得到上述方程具有无穷级解的判定条件,并对解的超级进行了估计.这里的P(z)为非零多项式,当P(z)为特定形式的多项式时,A_s可取为Airy函数,Weber-Hermite函数或指数函数.     

一类高阶线性微分方程解的增长性（英文）

In this paper, we investigate the growth of solutions of the differential equations f~((k))+ A_(k-1)(z)f~((k-1))+ ··· + A_0(z)f = 0, where A_j(z)(j = 0, ···, k-1) are entire functions.When there exists some coefficient A_s(z)(s ∈ {1, ···, k-1}) being a nonzero solution of f'+P(z)f = 0, where P(z) is a polynomial with degree n(≥ 1) and A_0(z) satisfies σ(A_0) ≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order.     

一类整函数系数微分方程解的复振荡

本文研究了微分方程f~(k) A_((k-1))f~((k-1)) … A_0f=F(k≥2)解的增长级和零点收敛指数,其中A_j=B_je~(P_j),j=0,1,…,k-1,B_j(z)为整函数,P_j(z)为多项式,σ(B_j)＜degP_j．     

系数的级相同的高阶微分方程解的增长性

In this paper,we consider the growth of solutions of some homogeneous and nonhomogeneous higher order differential equations.It is proved that under some conditions for entire functions F,A_(ji) and polynomials P_j(z),Q_j(z)(j=0,1,…,k-1;i=1,2)with degree n≥1,the equation f~(k)+(A_(k-1,1)(z)e~(p_(k-1)(z))+A_(k-1,2)(z)e~(Q_(k-1(z)))/~f~(k-1)+…+(A_(0,1)(z)e~(P_o(z))+A_(0,2)(z)e~(Q_0(z)))f=F,where k≥2,satisfies the properties:When F ≡0,all the non-zero solutions are of infinite order;when F=0,there exists at most one exceptional solution fo with finite order,and all other solutions satisfy λ(f)=λ(f)=σ(f)=∞.     

C上和?内某类高阶线性微分方程解的增长性

本文分别在复平面C上和单位圆△内考虑方程f~(k)+A_((k-1))(z)f~(k-1)+…+A_1(z)f'+A_0(z)f=0的解的增长性与其系数的增长性之间的关系.当A_0(z)或某个A_j(z)(0jk)严格控制其它系数时,通过比较A_0(z)和A_j(z)的迭代下级或迭代下型,得到上述方程当系数分别为整函数和单位圆△内解析函数时解的增长性的一些估计.     

一类离散m点边值问题正解的存在性和多重性

运用锥拉伸与锥压缩的Krasnosel’skii不动点定理,讨论了一类离散m点边值问题Δ2u(k)+λa(k)f(u(k))=0,k∈N,Δu(0)=∑m-2i=1biΔu(li),u(T+2)=∑m-2i=1aiu(li).在不要求极限li mu→0f(u)u,lui→m∞f(uu)存在的情形下,得到了其正解的存在性、非存在性和多重性的充分条件,推广了文[1]的相应结果.     

On the Growth of Solutions of a Class of Higher Order Linear Differential Equations

In this paper, we investigate the growth of solutions of the differential equations f(k)+Ak?1(z)f(k?1)+· · ·+A0(z)f =0, where Aj(z)(j=0, · · · , k?1) are entire functions. When there exists some coe?cient As(z)(s ∈ {1, · · · , k?1}) being a nonzero solution of f00+P(z)f =0, where P(z) is a polynomial with degree n(≥1) and A0(z) satisfiesσ(A0)≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order.     

一种两点迭代法

本文给出了一个求超越方程实根的新的两点格式ｘｋ＋１＝ｘｋ－ｘｋ－ｘｋ－１３ｆ（ｘｋ）－４ｆｘｋ＋ｘｋ－１２＋ｆ（ｘｋ－１）ｆ（ｘｋ），它集弦割法和抛物线法的优点于一身，具有更快的收敛速度，且收敛阶为二阶．     

Resonance Problem for a Class of Duffing’s Equations

Consider the Duffing's equation+g(x)=f(t),(1)where g∈C(R,R)and f∈P≡{f∈C(R,R);f is ω-periodic for some ω>0}.The functiong is said to be resonant if there exists f∈P such that eq.(1) has no bounded solutions on[0,∞).Using a generalized version of the Poincare-Birkhoff fixed point theorem,theauthors establish conditions on g which guarantee the following result holds:for any f∈Pwith period ω,there exists K≥0 such that eq.(1) has infinitely many kω-periodic solutionsfor every integer k≥K.In such a case,g is clearly non-resonant.     

Existence and Comparison Results for First Order Periodic Implicit Difference Equations with Maxima

In this paper, we establish comparison results (maximum principles) which allow us to use the monotone method and the method of upper and lower solutions in order to build convergent sequences to the solutions of difference equations of the type j u k = f k , u k +1 , max l ] { k m h +1,…, k +1} u l , k ] I , u 0 = u T , with j u k = u k +1 m u k , I ={0,1,…, T m 1} and f ] C ( I 2 R 2 R , R ).     

Nonlinear Boundary Value Problems on Sequence Spaces

In this paper we study the solvability of nonlinear, discrete-time boundary value problems for functional equations. Conditions are established for the existence of solutions to problems of the form $$x(k + 1) = f(k, x(k)) + \lambda g(k, x(k)); \quad k = 0, 1, 2, \ldots$$     

双特征的Beltrami方程和拟正则映射

设Ω为Ｒｎ上的一个区域，ｎ２，对于具有双特征矩阵Ｇ（ｘ），Ｈ（ｘ）∈Ｃｋ，α（Ω，Ｒｎ），ｋ１，０＜α＜１的Ｂｅｌｔｒａｍｉ方程（１．４），建立了在Ｓｏｂｏｌｅｖ空间Ｗ１，ｎｌｏｃ（Ω，Ｒｎ）上广义解的正则性：ｆ（ｘ）∈Ｃｋ＋１，δｌｏｃ（Ω），对某一δ：０＜δ＜１．     

某类高阶周期线性微分方程解的性质

本文研究了一类高阶周期系数线性微分方程解的性质问题. 利用复分析的相关理论和方法, 获得了在一些假设条件下, 当方程的系数 As 起控制作用时, 方程 f(k) + Ak-2f(k-2) + ...+Asf(s) + ... + A0f = 0 的任意两个线性无关解 f1,f2 满足λe(f1f2) ≥σe(As) 的结果, 推广了肖丽鹏的一个结果.     

一类高阶线性微分方程解的增长性

本文研究了在Aj(z),aj(j=0,1,…,k-1)满足一些条件下方程f(k)+Ak-1(z)eak-1f(k-1)+…+A0(z)ea0zf=0解的超级和在Aj(z),Pj(j)(j=0,1,…,k-1)满足一些条件下方程f(k)+Ak-1(z)ePk-1(z)f(k-1)+…+Aj(z)eajzf(j)+…+A0(z)eP0(z)f=0解的级。