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 - <p style="text-align: justify;">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.</p>