title: Anisotropic Picone identities and anisotropic Hardy inequalities.
abstract: In this paper, we derive an anisotropic Picone identity for the anisotropic Laplacian, which contains some known Picone identities. As applications, a Sturmian comparison principle to the anisotropic elliptic equation and an anisotropic Hardy type inequality are shown.
authors.affiliation: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
authors.forename: Tingfu
authors.initials: T
authors.lastname: Feng
authors.affiliation: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
authors.forename: Xuewei
authors.initials: X
authors.lastname: Cui
keywords: Sturmian comparison principle; anisotropic Hardy type inequality; anisotropic Picone identity; anisotropic elliptic equation