On complex oscillation and a problem of Ozawa (Q1086729)

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.