Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 108, pp. 1-11.
Title: Relations between the small functions and the solutions of
certain second-order differential equations
Authors: Huifang Liu (South China Normal Univ., Guangzhou, China)
Zhiqiang Mao (South China Normal Univ., Guangzhou, China)
Abstract:
In this paper, we investigate the relations between the small
functions and the solutions, first, second derivatives, and differential
polynomial of the solutions to the differential equation
$$
f''+A_1e^{P(z)}f'+A_0e^{Q(z)}f=0,
$$
where $P(z)=a_nz^n+\dots+a_0$, $Q(z)=b_nz^n+\dots+b_0$ are polynomials
with degree $n$ ($n\geq1$),
$a_i$, $b_i$ ($i=0,1,\dots,n$), $a_nb_n\neq 0$ are complex constants,
$A_j(z)\not \equiv 0$ ($j=0,1$) are entire functions with $\sigma(A_j)