Baouendi-Grushin p-退化椭圆算子的广义Picone恒等式及其应用  

On Generalized Picone's Identity and Its Applications for Baouendi-Grushin Operators

作　　者：王胜军[1] 韩亚洲[2] WANG Sheng-jun;HAN Ya-zhou(Department of Mathematics,Qinghai Normal University,Xining Qinghai 810008,China;Department of Mathematics,China Jiliang University,Hangzhou Zhejiang 310018,China)

机构地区：[1]青海师范大学数学与信息科学系,西宁810008 [2]中国计量学院数学系,杭州310018

出　　处：《西南师范大学学报（自然科学版）》2018年第3期1-6,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11201443)

摘　　要：建立了Baouendi-Grushin p-退化椭圆算子的广义Picone恒等式.作为应用,给出了Hardy不等式、Sturmium比较原理、主特征值的单调性结论和Liouville型结果.最后,讨论了具有奇异项的拟线性方程的弱解问题.In this paper,we establish a generalized version of the Picone’s identityfor Baouendi-Grushin operators.As applications,Hardy type inequality,Sturmian Comparison principle,strict monotonicity of the principal eigenvalue and a Liouville type theorem are gived.quasilinear system with singular nonlinearity is also studied.

关 键 词：Baouendi-Grushin p-退化椭圆算子 广义Picone恒等式 HARDY不等式 Sturmium比较原理 主特征值单调性 LIOUVILLE型定理 

分 类 号：O178[理学—数学]