含有可变指数的椭圆型方程的Pohozaev恒等式及其应用  

POHOZAEV-TYPE IDENTITY OF ELLIPTIC EQUATIONS WITH VARIABLE EXPONENTS AND SOME APPLICATONS

作　　者：马培 郑田田 Ma Pei;Zheng Tiantian(College of Science,Nanjing Forestry University,Nanjing 210037;Department of Mathematics,Jinling Institute of Technology,Nanjing 211169)

机构地区：[1]南京林业大学理学院,南京210037 [2]金陵科技学院理学院,南京211169

出　　处：《南京大学学报（数学半年刊）》2022年第2期146-154,共9页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：Supported by NSFC(No.11571176,No.12001274)。

摘　　要：本文中,我们建立了P(x)-双调和算子的Pohozaev型恒等式.利用这个恒等式,我们证明了比星形区域更一般的正型区域内一类变指数椭圆型方程正解的不存在性.In this work,we establish the Pohozaev-type identity of the P(x)-biharmonic operator.Using this identity,we prove that there are no positive solutions for a class of elliptic equations with variable exponents in positive-type domains that are more general than star-shaped ones.

关 键 词：P(x)-双调和算子 不存在性 Pohozaev型恒等式 正型区域 

分 类 号：O175.25[理学—数学] O177.91[理学—基础数学]