The infinite growth of solutions of second order linear complex differential equations with completely regular growth coefficient
Bull. Korean Math. Soc.
Published online September 7, 2020
Guowei Zhang
Anyang Normal University
Abstract : In this paper we discussed the classical problem of finding conditions on the entire coefficients A(z)
and B(z) guaranteeing that all nontrivial solutions of f′′ + A(z)f′ + B(z)f = 0 are of infinite order.
We assume A(z) is an entire function of completely regular growth and B(z) satisfies three different
conditions, then we obtain three results respectively. The three conditions are (1) B(z) has dynamical
property with a multiply connected Fatou component, (2) B(z) satisfies T(r, B) ∼ log M(r, B) outside
a set of finite logarithmic measure, (3) B(z) is extremal for Denjoy’s conjecture.
Keywords : entire function, infinite order, complex differential equation.
MSC numbers : 30D35; 34M10; 37F10.
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