Palais-Smale sequences for the fractional CR Yamabe functional and multiplicity results

TL;DR

This paper investigates the fractional CR Yamabe functional on the sphere, analyzing Palais-Smale sequences to understand bubbling phenomena and establishing the existence of infinitely many solutions.

Contribution

It provides new insights into the behavior of Palais-Smale sequences and proves the existence of infinitely many solutions for the fractional CR Yamabe equation.

Findings

Analysis of Palais-Smale sequences reveals bubbling phenomena.

Proves existence of infinitely many solutions to the fractional CR Yamabe equation.

Establishes multiplicity results for solutions on the sphere.

Abstract

In this paper we consider the functional whose critical points are solutions of the fractional CR Yamabe type equation on the sphere. We firstly study the behavior of the Palais-Smale sequences characterizing the bubbling phenomena and therefore we prove a multiplicity type result by showing the existence of infinitely many solutions to the related equation.