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

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

The Picone-type identity for the half-linear second order partial differential equation n i=1 ∂ ∂xi Φ ∂u ∂xi + c(x)Φ(u) = 0, Φ(u) := |u|u, p > 1, is established and some applications of this identity are suggested.

In this article, we study a class of doubly nonlinear parabolic problems involving the fractional p-Laplace operator. For problem, discuss existence, uniqueness and regularity weak solutions by using time-discretization method monotone arguments. global solutions, also prove stabilization results accretivity suitable associated This property is strongly linked to Picone identity that provides f...

This paper infers from a generalized Picone identity the uniqueness of stable positive solution for class semilinear equations superlinear indefinite type, as well and global attractivity coexistence state in two diffusive prototypes symbiotic competing species models Lotka–Volterra. The optimality these theorems reveals tremendous strength identity.

originates in the works of Mirzov [17] and Elbert [5], who named these equations `half linear’. This theory extends various aspects of oscillation theory, such as the Picone identity [10], Sturm comparison theorem [16, 17], oscillation and nonoscillation criteria of Kneser type [16] and Hille type [14], and other oscillation criteria [3]. One branch of this research is the study of the eigenval...

In this work we derive oscillation and nonoscillation criteria for the one dimensional p-laplacian in terms of an eigenvalue inequality for a mixed problem. We generalize the results obtained in the linear case by Nehari and Willet, and the proof is based on a Picone type identity.