Volume 47, Issue 3
Landau-Type Theorems for Solutions of a Quasilinear Differential Equation

J. Math. Study, 47 (2014), pp. 295-304.

Published online: 2014-09

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• 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.

• Keywords

Harmonic mapping, biharmonic mapping, Landau's theorem, quasilinear differential equation.

30C99, 30C62

mujingjing123@163.com (Jingjing Mu)

chxtt@hqu.edu.cn (Xingdi Chen)

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@Article{JMS-47-295, author = {Jingjing and Mu and mujingjing123@163.com and 8012 and Department of Mathematics, Huaqiao University, Quanzhou, Fujian 362021, P.R. China and Jingjing Mu and Xingdi and Chen and chxtt@hqu.edu.cn and 8013 and Department of Mathematics, Huaqiao University, Quanzhou, Fujian 362021, P.R. China and Xingdi Chen}, 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.

Jingjing Mu & Xingdi Chen. (2020). 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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