Simplicity of the the first eigenvalue of (p,q) nonlinear elliptic system

TL;DR

This paper provides an alternative proof demonstrating that the first eigenvalue of a nonlinear (p,q) elliptic system is simple, ensuring the uniqueness of the associated eigenfunctions up to scalar multiples.

Contribution

It offers a new proof for the simplicity of the first eigenvalue in nonlinear (p,q) elliptic systems, confirming eigenfunction uniqueness.

Findings

First eigenvalue is simple in the nonlinear system

Eigenfunctions are unique up to scaling

Alternative proof method established

Abstract

In this short note, the simplicity of the first eigenvalue of a nonlinear system is shown by an alternative proof; thereby, it states that the first eigenfunctions are unique up to modulo scaling.