Convergence for the fractional $p$-Laplacian and its corresponding extended Nirenberg problem

TL;DR

This paper investigates the convergence behavior of the fractional p-Laplacian for nonnegative functions with p>2 and explores blow-up phenomena in solutions to an extended Nirenberg problem involving this operator.

Contribution

It establishes convergence results for the fractional p-Laplacian and analyzes blow-up phenomena in solutions to the extended Nirenberg problem with negative prescribed functions.

Findings

Convergence of fractional p-Laplacian for nonnegative sequences with p>2.

Identification of blow-up phenomena in solutions to the extended Nirenberg problem.

Insights into the behavior of solutions with negative prescribed functions.

Abstract

The main objective of this paper is to establish the convergence for the fractional $p$-Laplacian of nonnegative sequence of functions with $p>2$. Further, we show the blow-up phenomena for solutions to the extended Nirenberg problem modeled by fractional $p$-Laplacian with the prescribed negative functions.