On the complex oscillation of meromorphic solutions of second order linear differential equations in the unit disc

Abstract

The main purpose of this paper is to investigate the oscillation theory of meromorphic solutions of the second order linear differential equation f + A(z) f = 0 for the case where A is meromorphic in the unit disc D = {z: |z| < 1}.

Value Distribution and Arbitrary-Order Derivatives of Meromorphic Solutions of Complex Linear Differential Equations in the Unit Disc

“…Firstly, we introduce some definitions on the growth and the value distribution of fast-growing meromorphic functions in ∆ (see, e.g., [4][5][6][7][8][9]). Definition 1 ([6]).…”

“…On the one hand, complex linear differential equations in ∆ have many similar properties to those in C. On the other hand, it is much more difficult to study complex linear differential equations in ∆ than in C, due to the lack of corresponding effective tools. Some results on this topic can be seen in, for example, [4][5][6][7][8][9][13][14][15][16][17][18][19][20].…”

Growth and oscillation of polynomial of linearly independent meromorphic solutions of second order linear differential equations in the unit disc

“…The growth and oscillation theory of complex differential equation (1.1) in the complex plane were firstly investigated by Laine in 1982-1983 (see [1,2]). After their many authors (see [5,7,8,9,14,15,17]) have investigated the complex differential equation (1.1) in the unit disc ∆ and in the complex plane. Recently in [17], the authors have investigated the relations between the polynomial of solutions of (1.1) and small functions in the complex plane.…”

“…[8]). For a ∈ C = C ∪ {∞}, the deficiency of a with respect to a meromorphic function f in ∆ is defined as δ(a, f ) = lim inf…”