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http://dx.doi.org/10.4134/BKMS.b200321

THE INFINITE GROWTH OF SOLUTIONS OF SECOND ORDER LINEAR COMPLEX DIFFERENTIAL EQUATIONS WITH COMPLETELY REGULAR GROWTH COEFFICIENT  

Zhang, Guowei (School of Mathematics and Statistics Anyang Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.2, 2021 , pp. 419-431 More about this Journal
Abstract
In this paper we discuss 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 a 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;
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