Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 635604, 9 pages
doi:10.1155/2011/635604
Research Article

On the Growth of Solutions of Some Second-Order Linear Differential Equations

School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

Received 10 December 2010; Accepted 9 February 2011

Academic Editor: Alberto Cabada

Copyright © 2011 Feng Peng and Zong-Xuan Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the growth of solutions of 𝑓 + 𝑃 ( 𝑧 ) 𝑓 + 𝑄 ( 𝑧 ) 𝑓 = 0 , where 𝑃 ( 𝑧 ) and 𝑄 ( 𝑧 ) are entire functions. When 𝑃 ( 𝑧 ) = 𝑒 𝑧 and 𝑄 ( 𝑧 ) = 𝐴 1 ( 𝑧 ) 𝑒 𝑎 1 𝑧 + 𝐴 2 ( 𝑧 ) 𝑒 𝑎 2 𝑧 satisfy some conditions, we prove that every nonzero solution of the above equation has infinite order and hyper-order 1, which improve the previous results.