International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 52583, 11 pages
doi:10.1155/IJMMS/2006/52583
Interaction between coefficient conditions and solution conditions
of differential equations in the unit disk
1Department of Mathematics, University of Tampa, Tampa 33606, FL, USA
2Department of Mathematical Sciences, Northern Illinois University, DeKalb 60115, IL, USA
Received 17 September 2005; Revised 7 June 2006; Accepted 22 June 2006
Copyright © 2006 K. E. Fowler and L. R. Sons. 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
The influence of the normality of the coefficient A(z) of the differential equation f(k)+A(z)f=0 on a solution f and also the influence of the normality of a solution f on A(z) are investigated in the unit disk. In particular, an estimate of P.
Lappan is used to determine restrictions on the growth of a
meromorphic function A(z) when a solution f is α-normal.