On zeros of solutions of higher order homogeneous linear differential equations

In this article, we investigate the exponent of convergence of zeros of solutions for some higher-order homogeneous linear differential equation, and prove that if A_k−1 is the dominant coefficient, then every transcendental solution f(z) of equation

f(k)+A_k-1 f(k-1)+?+A₀ f=0$f^{(k)}+A_{k-1}\hspace{0.17em}{f}^{(k-1)}+?+A_0\hspace{0.17em}f=0$

satisfies λ(f) = ∞, where λ(f) denotes the exponent of convergence of zeros of the meromorphic function f(z).     

ON THE DIFFERENCE COUNTERPART OF BRUCK＇S CONJECTURE

In this article, for a transcendental entire function f（z） of finite order which has a finite Borel exceptional value a, we utilize properties of complex difference equations to prove the difference counterpart of Bruck＇s conjecture, that is, if △f（z） = f（z ＋ η） - f（z） and f（z） share one value a （≠α） CM, where η ∈ C is a constant such that f（z ＋η） ≠ f（z）,then
△f（z）-a/f（z）-a=a/a-α.     

ON THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATION

In this paper, we consider a higher order differential equation and obtain a precise estimate of the order of growth and the hyper-order of solutions to the equation.     

Limiting directions of julia sets of entire solutions to complex differential equations

In this paper, we mainly investigate the dynamical properties of entire solutions of complex differential equations. With some conditions on coefficients, we prove that the set of common limiting directions of Julia sets of solutions, their derivatives and their primitives must have a definite range of measure.     

关于方程f″+Af=F(z)的复振荡

本文讨论了当A(z)为多项式,F(z)为具有无穷多个零点的整函数时,微分方程 f″+A(z)f=F(z)的解f(z)的复振荡的性质.     

PERTURBATION RESULTS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS

Two perturbation results on the linear differential function f" ∏(z)A(z)f = 0 areobtained, where ∏(z) and A(z) are periodic entire functions with period 2πi and σe(∏) ＜σe(A).     

ON THE DEPENDENT PROPERTY OF SOLUTIONS FOR HIGHER ORDER PERIODIC DIFFERENTIAL EQUATIONS

This article investigates the property of linearly dependence of solutions f(z) and f(z 2πi)for higher order linear differential equations with entire periodic coefficients.     

THE ZEROS AND ORDER OF MEROMORPHIC SOLUTIONS OF f^（k）＋Bf=H（z）

1.IntroductionandResultsConsidernon-homogeneouslineardifferentialequationsoftheform1.Lameprovedin[7]TheoremA.LetB(z),PO(z),PI(z)*06epolynomialssuchthatdegB=n21,degPO=p<(n k)/kandH=PI(z)epo('),then(a)IfdegPI相似文献