一类加权Kirchhoff方程非线性Liouville定理  

Nonlinear Liouville Theorems for a Weighted Kirchhoff Equation

作　　者：曹悦璠 方钟波[1] CAO Yuefan;FANG Zhongbo(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《应用数学》2021年第3期687-700,共14页Mathematica Applicata

基　　金：山东省自然科学基金面上项目(ZR2019MA072);中央高校基本科研基金(201964008)。

摘　　要：本文侧重研究一类加权Kirchhoff方程弱解及稳定解的非线性Liouville型定理.利用适当构造试验函数技巧,当非线性函数满足适当条件时,我们在加权函数空间中证明了该方程弱解的非存在性.同时,当非线性函数为指数型且加权函数满足适当条件时,建立了方程稳定解的非存在性结论.This paper is concerned with the nonlinear Liouville theorems of weak solution and stable solution for a weighted Kirchhoff equation.By the technique of test function,we prove the nonexistence of weak solution for the equation under some conditions of nonlinearity in the weighted space.Moreover,we establish the nonexistence results of stable solution to the equation with exponential growth when the weighted functions satisfy appropriate conditions.

关 键 词：KIRCHHOFF方程 加权函数 弱解 稳定解 非存在性 

分 类 号：O175.25[理学—数学]