Abstract This paper discusses equivalence conditions on entire solutions to eikonal-type nonlinear partial differential equations u z 1 2 + u z 2 2 = p ( z 1 , z 2 ) e g ( z 1 , z 2 ) in C 2 for polynomials g ( z 1 , z 2 ) , p ( z 1 , z 2 ) . All our results are supplemented by examples for accuracy.

中文翻译：

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关于 eikonal 型方程的全解

摘要 本文讨论了ekonal型非线性偏微分方程uz 1 2 + uz 2 2 = p ( z 1 , z 2 ) eg ( z 1 , z 2 ) in C 2 对于多项式g ( z 1 )的等价条件, z 2 ) , p ( z 1 , z 2 ) 。我们所有的结果都附有示例以确保准确性。