Journal of Inequalities and Applications
Volume 2005 (2005), Issue 5, Pages 469-478
On univalent solutions of the biharmonic equation
Department of Mathematics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates
Received 16 January 2004
Copyright © 2005 Z. AbdulHadi 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.
We analyze the univalence of the solutions of the biharmonic
equation. In particular, we show that if is a biharmonic map
in the form , , where is harmonic,
then is starlike whenever is starlike. In addition, when , , where and are harmonic,
we show that is locally univalent whenever is starlike and is orientation preserving.