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Entire solutions of a variation of the eikonal equation and related PDEs

Part of: Holomorphic functions of several complex variables General first-order equations and systems Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  07 May 2020

Feng Lü
Feng Lü*
Affiliation:
College of Science, China University of Petroleum, Qingdao, Shandong266580, P.R. China (lvfeng18@gmail.com)
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Abstract

The aim of this paper is twofold. The first aim is to describe the entire solutions of the partial differential equation (PDE) $u_{z_1}^2+2Bu_{z_1}u_{z_2}+u_{z_2}^2=e^g$, where B is a constant and g is a polynomial or an entire function in $\mathbb {C}^2$. The second aim is to consider the entire solutions of another PDE, which is a generalization of the well-known PDE of tubular surfaces.

Keywords

entire solutionFermat functional equationcharacteristic methodpartial differential equation

MSC classification

Primary: 30D30: Meromorphic functions, general theory
Secondary: 32A15: Entire functions 35F20: Nonlinear first-order equations 32A22: Nevanlinna theory (local); growth estimates; other inequalities
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 3 , August 2020 , pp. 697 - 708
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Copyright
Copyright © The Authors, 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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