Pohozaev identity for the fractional $p-$Laplacian on $\mathbb{R}^N$

TL;DR

This paper establishes a Pohozaev identity for fractional p-Laplacian problems on Euclidean space using approximation methods, and applies it to analyze energy levels of related nonlinear nonlocal equations.

Contribution

It introduces a novel Pohozaev identity for fractional p-Laplacian operators on ^N and demonstrates its application to energy functional analysis.

Findings

Proves a Pohozaev identity for fractional p-Laplacian on ^N.

Shows certain energy levels of the associated functional coincide.

Provides a new tool for studying nonlinear nonlocal problems.

Abstract

By virtue of a suitable approximation argument, we prove a Pohozaev identity for nonlinear nonlocal problems on $\mathbb{R}^N$ involving the fractional $p-$Laplacian operator. Furthermore we provide an application of the identity to show that some relevant levels of the energy functional associated with the problem coincide.