Energy estimated frequencies of standing-wave solutions to non-linear Klein-Gordon systems in higher dimension

TL;DR

This paper investigates the frequencies of standing-wave solutions in higher-dimensional non-linear Klein-Gordon systems, establishing existence results under minimal assumptions on the non-linear terms.

Contribution

It introduces a minimal assumption on the Sobolev sub-critical term that guarantees the existence of standing-waves through energy functional estimates.

Findings

Existence of standing-wave solutions established

Minimal assumptions on non-linear terms identified

Frequency estimates for solutions derived

Abstract

In this work a system of non-linear elliptic equations is considered, where the non-linear term is the sum of a quadratic form and a Sobolev sub-critical term. An extra assumption is introduced on the sub-critical term, which is minimal among the ones which guarantee the existence of standing-waves obtained by estimating frequencies of minimizing sequences with the energy functional.