On Petrenko's deviations and second order differential equations

Abstract

New results on the oscillation of solutions of $f''+A(z)f=0$ and on the growth of solutions of $f''+A(z)f'+B(z)f=0$ are obtained, where $A$ and $B$ are entire functions. Petrenko's magnitudes of deviation of $g$ with respect to $\infty$ play a key r\^ole in the results, where $g$ represents one of the coefficients $A$ or $B$. These quantities are defined by $\beta^-(\infty,g) = \liminf_{r\to\infty} \frac{\log M(r,g)}{T(r,g)}$ and $\beta^+(\infty,g) = \limsup_{r\to\infty} \frac{\log M(r,g)}{T(r,g)}$.