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 $\sigma(A_j)<n$.

Submitted February 12, 2007. Published August 07, 2007.
Math Subject Classifications: 34M10.
Key Words: Entire function; exponent of convergence of the zero-sequence.