含Grushin算子的加权椭圆系统稳定解的Liouville定理  

Liouville type theorem for stable solutions of the weighted elliptic system involving Grushin operator

作　　者：吴艳娟 甘怡清 胡良根 WU Yanjuan;GAN Yiqing;HU Lianggen(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《纯粹数学与应用数学》2023年第1期34-51,共18页Pure and Applied Mathematics

基　　金：国家自然科学基金(10671155,10112021).

摘　　要：考虑含Grushin算子的加权椭圆系统正稳定解的Liouville定理.首先建立这类椭圆系统稳定解的均值形式的判定准则,再建立新的比较原则,联合积分估计和Bootstrap迭代方法建立了权数指数不相等和指数为超临界时椭圆系统正稳定解的Liouville定理.The Liouville theorem for positive stable solutions of the weighted elliptic systems with Grushin operator is considered.Firstly,the criterion of the mean form for the stable solution of this kind of the elliptic system is established,and then a new comparison principle is established.By combining integral estimation and Bootstrap iteration,Liouville theorem for positive stable solution of the elliptic system with the unequal of the weight exponent and supercritical case is established.

关 键 词：Grushin算子 稳定解 LIOUVILLE定理 Bootstrap迭代 

分 类 号：O175[理学—数学]