Estimation of the hyper-order of entire solutions of complex linear ordinary differential equations whose coefficients are entire functions

The Zeros and Growth of Solutions of Higher Order Differential Equations

“…CONCLUSION In this paper, we shall investigate generalizations of problems of the above type to higher order homogeneous and non-homogeneous linear differential equations (2) and (3), and obtain the following results which extend the result of Chen and Belaïdi [2]. Theorem 2.1: Let H be a set of complex numbers satisfying dens{|z| : z ∈ H} > 0, and let A 0 (z), A 1 (z), .…”

“…The Proof of Theorem 2.3 Proof: Suppose that f ≡ 0 is a meromorphic solution of equation (2). By using the same arguments as in Theorem 2.1, we can get μ(f ) = σ(f ) = ∞ and σ 2 (f ) ≥ ξ − ε.…”

“…and investigated the growth and the hyper-order of solutions of equation (2). Recently, Yang [19] further investigated the growth of solutions of the equation…”

Estimates for the Green functions of nonautonomous higher order differential equations

“…Theorem 1.1 supplements the very interesting recent investigations of the asymptotic behavior of solutions of differential equations; cf. [1,2,11,13,16]. For the classical results, see [3] and the references therein.…”

Infinite order solutions of complex linear differential equations

“…It is well-known that all solutions of equation (1.1) are entire functions and if some of the coefficients of (1.1) are transcendental, then (1.1) has at least one solution with order .f / D C1: Recently, the growth theory of complex differential equations has been an active research area, and the growth problems of linear differential equations have an important aspect in this area. By defining the hyper-order [9,11], the growth of infinite order solutions of differential equations has been more precisely estimated (see [3,4,9]). Our starting point for this paper is a result by Kwon in [9]:…”