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On the growth of solutions of second order linear differential equations with extremal coefficients. (English) Zbl 1266.34140
The authors consider the second-order linear differential equation of the form \[ f''+A(z)f'+B(z)f = 0, \] where \(A\) and \(B\) are entire functions. The main result is that, if \(A\) is extremal for Yang’s inequality, in the sense that the number of finite deficient values is equal to half of the number of Borel directions, and if the orders of \(A\) and \(B\) are not the same, then every non-trivial solution \(f\) of the equation is of infinite order.

34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
Full Text: DOI
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