Fast Growing Solutions to Linear Differential Equations with Entire Coefficients Having the Same ρφ-order

Fast growing solutions of linear differential equations with analytic coefficients in the unit disc

“…The main purpose of this paper is to generalise Theorems 1.1, 1.2 and 1.5 by considering the concepts of the ϕ-orders and the ϕ-types. Our results are counterparts of theorems listed in [2,3,6], where the coefficients A j (z) in equation ( 1) are entire functions.…”

Growth of Meromorphic Solutions of General Complex Linear Differential-Difference Equation

“…[1,2,8,9,11,12,14]). Interestingly, we find there are many similar properties for both the case of complex linear differential equation (1) and the case of complex linear difference equation (2). We give examples on this topic as follows.…”

“…For the case of complex linear differential equation 1, Wu and Zheng [12] weakened the normal condition (see e.g. [1,11]) that only one dominant coefficient of (1) has the (lower) order or the (lower) type strictly greater than the order or the type of other coefficients, and obtained the following Theorems 1 and 2.…”

GROWTH OF \(\varphi\)–ORDER SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS ON THE COMPLEX PLANE

“…From this inequality, by the monotonicity of ϕ and (3.3), we obtain ρ 1 ϕ (f ) ≤λ 1 ϕ (f ). In addition, we have by definition thatλ 1 By Karamata's theorem (see [19]), it follows that ϕ(e t ) = t o (1) as t → +∞. Hence,…”

“…In [16], Liu-Tu-Shi made a small modification in the original definition of [p, q]-order introduced by Juneja-Kapoor-Bajpai [11] in order to study the growth of entire solutions of equations (1.1) and (1.2). After that, Li and Cao [15] investigated the growth of meromorphic solutions of equations (1.1) and (1.2) with meromorphic coefficients of [p, q]-order which improved many results in [3,5,13,16].…”