# Nonlinear Picone identities to Pseudo $p$-Laplace operator and applications

Document Type: Research Paper

Authors

Department of Applied Mathematics‎, ‎Northwestern Polytechnical University‎, ‎Xi'an‎, ‎Shaanxi‎, ‎710072‎, ‎P.R‎. ‎China.

Abstract

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight and remainder term, a nonnegative estimate of the functional associated to pseudo p-Laplace equation.

Keywords

Main Subjects

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### History

• Receive Date: 07 October 2016
• Revise Date: 10 December 2017
• Accept Date: 10 December 2017