Nondegeneracy of the entire solution for the $N$-Laplace Liouville equation

TL;DR

This paper proves the nondegeneracy of a specific explicit finite-mass solution to the $N$-Laplace Liouville equation on the entire space, establishing its uniqueness up to scaling and translation.

Contribution

It demonstrates the nondegeneracy of the explicit solution, confirming its uniqueness properties in the context of the $N$-Laplace Liouville equation.

Findings

Proves the nondegeneracy of the explicit finite-mass solution.

Confirms the solution's uniqueness up to scaling and translation.

Establishes foundational properties of solutions to the $N$-Laplace Liouville equation.

Abstract

In this note, we prove the nondegenracy of the explicit finite-mass solution to the $N$-Laplace Liouville equation on the whole space, which is recently shown to be unique up to scaling and translation.