The hyper-order of solutions of certain linear complex differential equations

On the hyper-order of solutions of two class of complex linear differential equations

ON 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...

On the hyper order of solutions of a class of higher order linear differential equations

In this paper, we investigate the order and the hyper order of entire solutions of the higher order linear differential equation f +Ak−1 (z) e k−1f +...+A1 (z) e 1f ′ +A0 (z) e 0f = 0 (k ≥ 2) , where Pj (z) (j = 0, ..., k − 1) are nonconstant polynomials such that degPj = n (j = 0, ..., k − 1) and Aj (z) ( ≡ 0) (j = 0, ..., k − 1) are entire functions with ρ (Aj) < n (j = 0, ..., k − 1). Under ...

Entire Functions of Finite Order as Solutions to Certain Complex Linear Differential Equations

When is an entire function of finite order a solution to a complex 2nd order homogeneous linear differential equation with polynomial coefficients? In this paper we will give two (equivalent) answers to this question. The starting point of both answers is the Hadamard product representation of a given entire function of finite order. While the first answer involves certain Stieltjes-like relati...

On the Hyper-order of Solutions of Second Order Linear Differential Equations with Meromorphic Coefficients

In this paper, we investigate the growth of solutions of the linear differential equation 0 = Bf f A f      , where ) (z A and 0) )( (  z B are meromorphic functions. More specifically, we estimate the lower bounded of hyperorder of solutions of the equation with respect to the conditions of ) (z A and 0) )( (  z B if solutions 0 ( f ) of the equation is of infinite order. keywords: ...