International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 52583, 11 pages

Interaction between coefficient conditions and solution conditions of differential equations in the unit disk

K. E. Fowler1 and L. R. Sons2

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.


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.