Interaction between coefficient conditions and solution conditions of differential equations in the unit disk. (English) Zbl 1142.30013
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 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.
Reviewer: Jagdish Prakash (Mumbai)
MSC:
| 30D45 | Normal functions of one complex variable, normal families |
| 34M05 | Entire and meromorphic solutions to ordinary differential equations in the complex domain |
| 34M10 | Oscillation, growth of solutions to ordinary differential equations in the complex domain |
Keywords:
normal functionCitations:
Zbl 0387.30018References:
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