论文标题
关于Petrenko的偏差和二阶微分方程
On Petrenko's deviations and second order differential equations
论文作者
论文摘要
获得$ f'''+a（z）f = 0 $的解决方案的振荡以及$ f'''+a（z）f'+b（z）f = 0 $的溶液增长的新结果，其中$ a $ a $ a $ a $ b $是整个功能。 Petrenko相对于$ \ infty $的$ g $偏差的幅度在结果中播放了一个键rôle，其中$ g $代表系数$ a $ a $ a $ a $ a $ a或$ b $。这些数量由$β^ - （\ infty，g）= \ liminf_ {r \ to \ infty} \ frac {\ log M（r，g）} { m（r，g）} {t（r，g）} $。
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 rôle in the results, where $g$ represents one of the coefficients $A$ or $B$. These quantities are defined by $β^-(\infty,g) = \liminf_{r\to\infty} \frac{\log M(r,g)}{T(r,g)}$ and $β^+(\infty,g) = \limsup_{r\to\infty} \frac{\log M(r,g)}{T(r,g)}$.
