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On univalent solutions of the biharmonic equation

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.

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Correspondence to Z AbdulHadi.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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AbdulHadi, Z., Abu Muhanna, Y. & Khuri, S. On univalent solutions of the biharmonic equation. J Inequal Appl 2005, 642561 (2005). https://doi.org/10.1155/JIA.2005.469

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