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

Authors

  • M. Yu Department of Applied Mathematics‎, ‎Northwestern Polytechnical University‎, ‎Xi'an‎, ‎Shaanxi‎, ‎710072‎, ‎P.R‎. ‎China.
  • T. Feng 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.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Anisotropic Picone identities and anisotropic Hardy inequalities

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.

full text

Picone-type Identity for Pseudo P-laplacian with Variable Power

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.

full text

Mini-Workshop: Nonlinear Spectral and Eigenvalue Theory with Applications to the p-Laplace Operator Table of Contents

Asymmetric Eigenvalue Problems with Weights for the p-laplacian with Neumann Boundary Conditions M. Cuesta (Calais) (joint work with M. Arias (Granada), J.-P. Gossez (Bruxelles)) The motivation of this work is the study of (1) −∆pu = f(x, u) in Ω, ∂u ∂n = 0 on ∂Ω, where ∆pu := div(|∇u|p−2∇u), 1 < p < ∞, and Ω is a bounded smooth domain of R and |f(x, s)| ≤ a(x)|s|p−1 + b(x) with a, b belonging ...

full text

p-brane solutions and Beltrami-Laplace operator

Generalization of the harmonic superposition rule for the case of dependent choice of harmonic functions is given. Dependence of harmonic functions from all (relative and overall) transverse coordinates is considered using the BeltramiLaplace operator. Supersymmetry of IIB 10D supergravity solutions with only non-vanished 5-form field and 11D supergravity solutions is discussed.

full text

Quasiregular mappings and the p-Laplace operator

We describe the role of p-harmonic functions in the theory of quasiregular mappings.

full text

Maximal Mean Exit Time Related To The p-Laplace Operator∗

In this paper we introduce a boundary value problem involving powers of the p-Laplace operator. We will then prove a variant of Talenti inequality which shows that the Schwarz symmetrization of the solution of the boundary value problem is majorized by the solution of the appropriately symmetrized version of the problem. The case of equality is also investigated. Finally, as an application, we ...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 43  issue 7

pages  2517- 2530

publication date 2017-12-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023