Existence of positive solutions to a semi-linear elliptic system with a small energy/charge ratio

TL;DR

This paper proves the existence of positive solutions for a system of nonlinear elliptic equations associated with Klein-Gordon systems, focusing on solutions with a small energy-to-charge ratio.

Contribution

It establishes the existence of positive solutions characterized by a small energy/charge ratio for a nonlinear elliptic system related to Klein-Gordon equations.

Findings

Existence of positive solutions with small energy/charge ratio.

Solutions correspond to standing-wave k-tuples in Klein-Gordon systems.

Theoretical proof of solution existence under specified conditions.

Abstract

We prove the existence of positive solutions to a sys- tem of k non-linear elliptic equations corresponding to standing- wave k-uples solutions to a system of non-linear Klein-Gordon equations. Our solutions are characterised by a small energy/charge ratio, appropriately defined.