Optimal decay for solutions of nonlocal semilinear equations with critical exponent in homogeneous group

TL;DR

This paper determines the precise decay rates of positive solutions to a Yamabe-type nonlocal equation on homogeneous Lie groups, extending understanding of asymptotic behavior in geometric analysis.

Contribution

It establishes the sharp asymptotic decay for solutions of a nonlocal Yamabe equation on homogeneous groups, linking nonlocal operators with geometric analysis.

Findings

Sharp decay rates of solutions are derived.

Results extend to a class of nonlocal operators in conformal CR geometry.

Provides a foundation for further geometric analysis on homogeneous groups.

Abstract

In this paper we establish the sharp asymptotic decay of positive solutions of the Yamabe type equation $\frlap u=u^{\frac{Q+2s}{Q-2s}}$ in a homogeneous Lie group, where $\frlap$ represents a suitable pseudodifferential operator modelled on a class of nonlocal operators arising in conformal CR geometry.