  It is known that, equally well in the unit disc as in the whole complex
plane, the growth of the analytic coefficients $A_0,\dotsc,A_{k-2}$ of
\begin{equation*} f^{(k)} + A_{k-2} f^{(k-2)} + \dotsb + A_1 f'+ A_0 f = 0,
\quad k\geq 2, \end{equation*} determines, under certain growth restrictions,
not only the growth but also the oscillation of its non-trivial solutions, and
vice versa. A uniform treatment of this principle is given in the disc
$D(0,R)$, $0<R\leq \infty$, by using several measures for growth that are more
flexible than those in the existing literature, and therefore permit more
detailed analysis. In particular, results obtained are not restricted to cases
where solutions are of finite (iterated) order of growth in the classical
sense. The new findings are based on an accurate integrated estimate for
logarithmic derivatives of meromorphic functions, which preserves generality in
terms of three free parameters.
