On complex oscillation and a problem of Ozawa

抄録

It is shown that if Q(z) is a non-constant polynomial, then all non-trivial solutions of
y''+(e^z+Q(z))y=0
have zeros with infinite exponent of convergence. Similar methods are used to settle a problem of M. Ozawa: if P(z) is a non-constant polynomial, all non-trivial solutions of
y''+e^−zy'+P(z)y=0
have infinite order.