一个新的非线性Picone恒等式及其应用(英文)  

A New Nonlinear Picone Identity and Applications

作　　者：冯廷福[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072

出　　处：《应用数学》2017年第2期278-283,共6页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11271299);the Natural Science Basic Research Plan in Shaanxi Province of China(2016JM1203)

摘　　要：本文建立一个新的非线性Picone恒等式,它包括一些已有的Picone恒等式.利用这个新的Picone恒等式,我们给出了带奇异项p-Laplace方程的Sturm比较原理,p-Laplace方程组的Liouville定理和带权Hardy不等式.由这里一般的带权Hardy型不等式,我们可以得到几个新的有趣的带权型Hardy不等式.In this paper, we derive a new nonlinear Picone identity to the p-Laplacian which contains some known Picone identities. As applications, a Sturmian comparison principle to the p-Laplace equation with singular item, a Liouville＇s theorem to the p-Laplace system and a general Hardy type inequality with weights are obtained. It yields some new and interesting Hardy type inequalities from the results here.

关 键 词：PICONE恒等式 P-LAPLACE算子 Sturm比较原理 LIOUVILLE定理 HARDY型不等式 

分 类 号：O178[理学—数学]