几类二次三项式偏微分方程的整函数解  

Entire Solutions of Some Quadratic Trinomial PartialDifferential Equations

作　　者：魏慧珍 涂金[1] 徐洪焱 WEI Huizhen;TU Jin;XU Hongyan(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,China;School of Mathematics and Computer Science,Shangrao Normal University,Shangrao 334001,China)

机构地区：[1]江西师范大学数学与统计学院,江西南昌330022 [2]上饶师范学院数学与计算机科学学院,江西上饶334001

出　　处：《应用数学》2024年第1期42-51,共10页Mathematica Applicata

基　　金：国家自然科学基金(11561031,12161074,11761035)。

摘　　要：文章主要运用值分布和偏微分方程特征方程方法研究了几类一阶、二阶以及混合型偏微分方程的整函数解,获得了涉及几类二次三项式偏微分方程有限级超越整函数解的存在性及其形式,推广了先前的结果,同时举例说明所得方程解的形式是准确的.By making use of the value distribution and the characteristic equation of partial differential equations,we mainly study the entire solutions of several kinds of first order,second order and their mixed type partial differential equations,and obtain the existence and forms of finite order transcendental entire solutions involving some quadratic trinomial partial differential equations.Our results are some generalization of the previous results,and some examples show that the forms of the solutions of the equations are correct.

关 键 词：整函数 偏微分方程 存在性 

分 类 号：O174.5[理学—数学]