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

J. J. Mu & X. D. Chen

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

  • AMS Subject Headings

30C99 30C62

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COPYRIGHT: © Global Science Press

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@Article{JMS-47-295, author = {J. J. Mu and X. D. 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} }
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