Landau-Type Theorems for Solutions of a Quasilinear Differential Equation

Authors

  • Jingjing Mu Department of Mathematics, Huaqiao University, Quanzhou, Fujian 362021, P.R. China
  • Xingdi Chen Department of Mathematics, Huaqiao University, Quanzhou, Fujian 362021, P.R. China

DOI:

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

Keywords:

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

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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Published

2014-09-02

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Issue

Vol. 47 No. 3 (2014)

Section

Articles

How to Cite

Landau-Type Theorems for Solutions of a Quasilinear Differential Equation. (2014). Journal of Mathematical Study, 47(3), 295-304. https://doi.org/10.4208/jms.v47n3.14.05