Bulletin of the
Korean Mathematical Society BKMS

In this paper, we consider the differential equation
\begin{equation*}
f''+Af'+Bf=0, (*)
\end{equation*}
where $A(z)$ and $B(z)\not\equiv 0$ are entire functions. Assume that $A(z)$ is a non-trivial solution of $\omega''+P(z)\omega=0$, where $P(z)$ is a polynomial. If $B(z)$ satisfies extremal for Yang's inequality and other conditions, then every non-trivial solution $f$ of equation (*) has $\mu(f)=\infty$. We also investigate the relation between a small function and a differential polynomial of $f$.

Keywords: differential equations, lower order, exponent of convergence of zeros, accumulation rays, differential polynomials

MSC numbers: 34M10, 30D35