On Landesman-Lazer conditions and the Fundamental Theorem of Algebra

TL;DR

This paper provides an elementary proof of a Landesman-Lazer type result for systems using a shooting argument and discusses its relation to the fundamental theorem of algebra.

Contribution

It introduces a new elementary proof technique for Landesman-Lazer results and connects these results to the fundamental theorem of algebra.

Findings

Elementary proof of Landesman-Lazer type result for systems

Connection established between Landesman-Lazer conditions and the fundamental theorem of algebra

Shooting method used as a key proof technique

Abstract

We give an elementary proof of a Landesman-Lazer type result for systems by means of a shooting argument and explore its connection with the fundamental theorem of algebra.