On a question of Gundersen concerning the growth of solutions of linear differential equations

Abstract

Abstract. We prove that every nontrivial solution of f ′′ + A(z)f ′ + Q(z)f = 0 is of infinite order, where A(z) is an entire function satisfying λ(A) < ρ(A) < ∞ and some restrictions, and Q(z) is a non-constant polynomial. This result gives partial solutions to a question posed by Gundersen.

Asymptotic integration theory for $f'' + P(z)f = 0$

“…The ideas in [12,Ch. 7.4] are profound, the methods are creative, and the results of the theory have been very useful in numerous applications to differential equations [3,5,6,7,8,16,18,19,20,21,24,27].…”

On [p,q]-order of growth of solutions of complex linear differential equations near a singular point

“…The growth of solutions of (1) is very interesting topic after Wittich's work [16], the main tool is Nevanlinna theory of meromorphic functions which can be found in [6,10,18]. Many results have been obtained by many different researchers, for the case of complex plane C, see, for example, [10][11][12][13]17] and therein references, for the case of unit disc D, see, for example [1,2,4,7,14] and therein references. Recently, Fettouch and Hamouda investigated the growth of solutions of equation (1) by using a new idea, in which the coefficients are analytic function except a finite singular point, more details can be found in [3,5].…”

Order and Hyper-order of Solutions of Second Order Linear Differential Equations

“…B. Wu, and Zhang gave conditions on the coefficients A(z) and B(z) so that all solutions f ( ≡ 0) are of infinite order. Their results can be found in [ [22], [23], [28], [29]]. In Kumar and Saini [16] we gave conditions on coefficients and proved the following theorem: Theorem 3.…”