Interaction between coefficient conditions and solution conditions of differential equations in the unit disk (Q2469034)

The influence of the normality of the coefficient \(A(z)\) of the differential equation \(f^{(k)}+A(z)f=0\) on a solution \(f\) and also the influence of the normality of a solution \(f\) on \(A(z)\) are investigated in the unit disk. In particular, an estimate of \textit{P. Lappan} [Ann. Acad. Sci. Fenn., Ser. A I 3, 301--310 (1977; Zbl 0387.30018)] is used to determine restrictions on the growth of a meromorphic function \(A(z)\) when a solution \(f\) is \(\alpha \)-normal.