Electron. J. Diff. Eqns., Vol. 2007(2007), No. 108, pp. 1-11.

Relations between the small functions and the solutions of certain second-order differential equations

Huifang Liu, Zhiqiang Mao

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 7, 2007.
Math Subject Classifications: 34M10.
Key Words: Entire function; exponent of convergence of the zero-sequence.

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Huifang Liu
School of Mathematics, South China Normal University
Guangzhou 510631, China.
Institute of Mathematics and Informatics
Jiangxi Normal University, Nanchang 330027, China
email: liuhuifang73@sina.com
Zhiqiang Mao
School of Mathematics, South China Normal University
Guangzhou 510631, China.
Depatment of Mathematics
Jiangxi Science and Teachers college, Nanchang 330013, China
email: maozhiqiang1@sina.com

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