A generalized nonlinear Picone identity for the p-biharmonic operator and its applications

Abstract

Abstract A generalized nonlinear Picone identity for the p-biharmonic operator is established in this paper. As applications, a Sturmian comparison principle to the p-biharmonic equation with singular term, a Liouville’s theorem to the p-biharmonic system, and a generalized Hardy–Rellich type inequality are obtained.

Keywords

• p-biharmonic operator
• Generalized nonlinear Picone identity
• Sturmian comparison principle
• Liouville’s theorem
• Hardy–Rellich type inequality