Growth of solutions of some second order differential equations with entire coefficients
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In this paper, we consider the differential equation \begin{equation*} f''+Af'+Bf=0, \leqno(*) \end{equation*} where $A(z)$ and $B(z)\not\equiv 0$ are entire functions. Assume that $A(z)$ is a transcendental 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 transcendental solution $f$ of equation (*) has $\mu(f)=\infty$. We also investigate the relation between a small function and a differential polynomial of $f$.
Abstract
In this paper, we consider the differential equation \begin{equation*} f''+Af'+Bf=0, \leqno(*) \end{equation*} where $A(z)$ and $B(z)\not\equiv 0$ are entire functions. Assume that $A(z)$ is a transcendental 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 transcendental solution $f$ of equation (*) has $\mu(f)=\infty$. We also investigate the relation between a small function and a differential polynomial of $f$.