论文标题
$ \ mathbb {c}^2 $的几种通用二次类型PDE和PDDE的先验整个解决方案
Transcendental entire solutions of several general quadratic type PDEs and PDDEs in $ \mathbb{C}^2 $
论文作者
论文摘要
功能方程$ f^2+g^2 = 1 $和$ f^2+2αfg+g^2 = 1 $分别称为fermat-type二项式和三项方程。了解一般二次函数方程的解决方案的存在和形式是很有趣的。在本文中，利用Nevanlinna的理论来实现几个复杂变量的理论，我们研究了$ $ af^2+2αfg+b g^2+b g^2+2βF+2βG+2γG+2γG+2γG+C = 0 $ in $ \ MATHBB in $ \ MATHBB c} c} c}^2 $ in $ af^2+2αfg+b g^2+2βF+2γG+c = 0 $的存在和形式的存在和形式。因此，我们获得了本文有关二项式方程的主要结果的某些推论，这些方程在[\ textit {rocky Mountain J. Math.} \ textbf {51}（6）（2021），2217-2235]中概括了许多结果。
The functional equations $ f^2+g^2=1 $ and $ f^2+2αfg+g^2=1 $ are respectively called Fermat-type binomial and trinomial equations. It is of interest to know about the existence and form of the solutions of general quadratic functional equations. Utilizing Nevanlinna's theory for several complex variables, in this paper, we study the existence and form of the solutions to the general quadratic partial differential or partial differential-difference equations of the form $ af^2+2αfg+b g^2+2βf+2γg+C=0 $ in $ \mathbb{C}^2 $. Consequently, we obtain certain corollaries of the main results of this paper concerning binomial equations which generalize many results in [\textit{Rocky Mountain J. Math.} \textbf{51}(6) (2021), 2217-2235] in the sense of arbitrary coefficients.
