Landau-Type Theorems for Solutions of a Quasilinear Differential Equation

Landau-Type Theorems for Solutions of a Quasilinear Differential Equation

Year:    2014

Author:    Jingjing Mu, Xingdi Chen

Journal of Mathematical Study, Vol. 47 (2014), Iss. 3 : pp. 295–304

Abstract

In this paper, we study solutions of the quasilinear differential equation $\bar{z}\partial_{\bar{z}}f(z)+z\partial_{z}f(z)+(1-|z|^2)\partial_{z}\partial_{\bar{z}}f(z)=f(z)$. We utilize harmonic mappings to obtain an explicit representation of solutions of this equation. By this result, we give two versions of Landau-type theorem under proper normalization conditions.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v47n3.14.05

Journal of Mathematical Study, Vol. 47 (2014), Iss. 3 : pp. 295–304

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Harmonic mapping biharmonic mapping Landau's theorem quasilinear differential equation.

Author Details

Jingjing Mu

Xingdi Chen

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