Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 416273, 12 pages
doi:10.1155/2009/416273
Research Article

Subnormal Solutions of Second-Order Nonhomogeneous Linear Differential Equations with Periodic Coefficients

Zhi-Bo Huang,1 Zong-Xuan Chen,1 and Qian Li2

1School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
2Department of Applied Mathematics, South China Agricultural University, Guangzhou 510640, China

Received 8 February 2009; Accepted 24 May 2009

Academic Editor: Kunquan Lan

Copyright © 2009 Zhi-Bo Huang et al. 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 obtain the representations of the subnormal solutions of nonhomogeneous linear differential equation f′′+[P1(ez)+Q1(e−z)]f′+[P2(ez)+Q2(e−z)]f=R1(ez)+R2(e−z), where P1(z),P2(z),Q1(z),Q2(z),R1(z), and R2(z) are polynomials in z such that P1(z),P2(z),Q1(z), and Q2(z) are not all constants, deg⁡P1>deg⁡P2. We partly resolve the question raised by G. G. Gundersen and E. M. Steinbart in 1994.