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

J. J. Mu and X. D. Chen


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

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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.

  • History

Published online: 2014-09

  • AMS Subject Headings

30C99, 30C62

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