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

Copyright

© AbdulHadi et al. 2005