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.

The authors derive an analog of the well-known Picone identity but for nonlinear dynamic equations on time scales. As a consequence, they obtain a nonlinear comparison theorem in the spirit of the classical Sturm–Picone comparison theorem. Comparison results yielding the nonoscillation of all solutions of nonlinear equations are also obtained. AMS subject classification: 34C10, 34C15, 39A11.

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 an...

Two identities of the Picone type for a class of half-linear differential systems in the plane are established and the Sturmian comparison theory for such systems is developed with the help of these new formulas.

By means of some Picone-type identity, we provide some simple oscillation criteria for the equations { a(t)φα(y ′) }′ + q(t)φβ(h(y)) = 0, t > 0; α, β > 0. Mathematics Subject Classification: 34C10, 34K15

In this article, a Picone-type identity for the weighted p-biharmonic operator is established and comparison results for a class of half-linear partial differential equations of fourth order based on this identity are derived.

In the article, we extend the well-known Picone identity for halflinear partial differential equations to equations with anisotropic p-Laplacian.

The aim of this article is to give Sturm-Picone type theorems for the pair of second order nonlinear elliptic differential equations div(p1(x)|∇u|∇u) + q1(x)f1(u) + r1(x)g1(u) = 0, div(p2(x)|∇v|∇v) + q2(x)f2(v) + r2(x)g2(v) = 0, where | · | denotes the Euclidean length and ∇ = ( ∂ ∂x1 , . . . , ∂ ∂xn )T (the superscript T denotes the transpose). Our results include some earlier results and gene...

A Picone type identity is established for homogeneous differential operators involving the pseudo p-Laplacian with variable exponent p = p(x). Using this identity, it is shown that the classical Sturmian theory extends to the associated partial differential equations.