Open Access

On univalent solutions of the biharmonic equation

Journal of Inequalities and Applications20052005:642561

https://doi.org/10.1155/JIA.2005.469

Received: 16 January 2004

Published: 31 October 2005

Abstract

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.

Authors’ Affiliations

(1)
Department of Mathematics, American University of Sharjah, Sharjah, United Arab Emirates

Copyright

© AbdulHadi et al. 2005