Landau-Type Theorems for Solutions of a Quasilinear Differential Equation
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@Article{JMS-47-295,
author = {Mu , Jingjing and Chen , Xingdi},
title = {Landau-Type Theorems for Solutions of a Quasilinear Differential Equation},
journal = {Journal of Mathematical Study},
year = {2014},
volume = {47},
number = {3},
pages = {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.
}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v47n3.14.05}, url = {http://global-sci.org/intro/article_detail/jms/9960.html} }
TY - JOUR
T1 - Landau-Type Theorems for Solutions of a Quasilinear Differential Equation
AU - Mu , Jingjing
AU - Chen , Xingdi
JO - Journal of Mathematical Study
VL - 3
SP - 295
EP - 304
PY - 2014
DA - 2014/09
SN - 47
DO - http://doi.org/10.4208/jms.v47n3.14.05
UR - https://global-sci.org/intro/article_detail/jms/9960.html
KW - Harmonic mapping, biharmonic mapping, Landau's theorem, quasilinear differential equation.
AB -
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.
Mu , Jingjing and Chen , Xingdi. (2014). Landau-Type Theorems for Solutions of a Quasilinear Differential Equation.
Journal of Mathematical Study. 47 (3).
295-304.
doi:10.4208/jms.v47n3.14.05
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