Nagoya Mathematical Journal

Entire solutions of $(u_{z_{1}})^{m}+(u_{z_{2}})^{n}=e^{g}$

Bao Qin Li

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The paper is concerned with description of entire solutions of the partial differential equations $u_{z_{1}}^{m}+u_{z_{2}}^{n}=e^{g}$, where $m \geq 2$, $n \geq 2$ are integers and $g$ is a polynomial or an entire function in ${\bf C}^{2}$. Descriptions are given and complemented by various examples.

Article information

Nagoya Math. J., Volume 178 (2005), 151-162.

First available in Project Euclid: 16 August 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35F20: Nonlinear first-order equations 32A15: Entire functions 32A22: Nevanlinna theory (local); growth estimates; other inequalities {For geometric theory, see 32H25, 32H30}


Li, Bao Qin. Entire solutions of $(u_{z_{1}})^{m}+(u_{z_{2}})^{n}=e^{g}$. Nagoya Math. J. 178 (2005), 151--162.

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