Growth of Solutions of Second Order Complex Linear Differential Equations with Entire Coefficients

Abstract

Some new conditions on the entire coefficients $A(z)$ and $B(z)$, which guarantee every nontrivial solution of $f''+A(z)f'+B(z)f=0$ is of infinite order, are given in this paper. Two classes of entire functions are involved in these conditions, the one is entire functions having Fabry gaps, the another is function extremal for Yang's inequality. Moreover, a kind of entire function having finite Borel exception value is considered.