Complex Oscillation of Entire Solutions of Higher-order Linear Differential Equations
نویسنده
چکیده
In this paper, we investigate higher-order linear differential equations with entire coefficients of iterated order. We improve and extend a result of Beläıdi and Hamouda by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen and the WinmanValiron theory. We also consider the nonhomogeneous linear differential equations by using the basic method and some lemmas from the present and other three authors.
منابع مشابه
Oscillation of Complex High Order Linear Differential Equations with Coefficients of Finite Iterated Order
In this paper, we investigate the growth of solutions of complex high order linear differential equations with entire or meromorphic coefficients of finite iterated order and we obtain some results which improve and extend some previous results of Z. X. Chen and L. Kinnunen.
متن کاملTheory of Hybrid Fractional Differential Equations with Complex Order
We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...
متن کاملOscillation of Higher-order Linear Differential Equations with Entire Coefficients
This article is devoted to studying the solutions to the differential equation f (k) +Ak−1(z)f (k−1) + · · ·+A0(z)f = 0, k ≥ 2, where coefficients Aj(z) are entire functions of integer order. We obtain estimates on the orders and the hyper orders of the solutions to the above equation.
متن کاملOscillation Results on Meromorphic Solutions of Second Order Differential Equations in the Complex Plane
The main purpose of this paper is to consider the oscillation theory on meromorphic solutions of second order linear differential equations of the form f ′′ + A(z)f = 0 where A is meromorphic in the complex plane. We improve and extend some oscillation results due to Bank and Laine, Kinnunen, Liang and Liu, and others.
متن کاملON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS
Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006