Abstract
In this paper, we study the growth of solutions of the second order linear complex differential equations insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .
Highlights
Since Wittich’s work in (1), the solution’s growth of linear complex differential equations became one of the interesting topics in complex analysis
The order of growth is used to measure the growth of entire functions
It is well known that all solutions of Eq (1) are entire functions provided thatA(z) andB(z) are entire functions, and if at least one of the coefficients is transcendental and f1, f2 are two linearly independent solutions of Eq (1), at least one of f1, f2 is of infinite order
Summary
Since Wittich’s work in (1), the solution’s growth of linear complex differential equations became one of the interesting topics in complex analysis. The concept due to Yang depends on the following result: Theorem 1 (4) Assume that f is entire function of lower finite order. Definition 5 (8) (Denjoy’s Conjecture) Let f be an entire function of finite order ρ.
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