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On complex oscillation and a problem of Ozawa. (English) Zbl 0609.34041
The author proves that if Q(z) is a non-constant polynomial and \(\alpha\in C\), then every nontrivial solution of \(y''+(e^{z+\alpha}+Q(z))y=0\) has zeros with infinite exponent of convergence. Similar methods are used to settle a problem of Ozawa: If P(z) is a non-constant polynomial, then all nontrivial solutions of \(y''+e^{-z}y'+P(z)y=0\) have infinite order.
Reviewer: P.Marušiak

MSC:
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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