Growth of Solutions of Second Order LinearComplex Differential Equations with CompletelyRegular Growth Coefficient

摘要

In this paper we investigate the classical problemof finding conditions on the entire coefficients A(z) and B(z) toensure that all nontrivial solutions of f′′ +A(z)f′ +B(z)f = 0are of infinite order. We assume A(z) is an entire function withcompletely regular growth and B(z) satisfies three conditionsrespectively, (1) B(z) is a transcendental entire function withlower order less than 1/2; (2) B(z) is a transcendentalentire function with Fabry gaps; (3) B(z) satisfies T(r, B) ～α log M(r, B) outside a set of finite logarithmic measure, weprove the solutions have infinite order in these three cases.