Finite energy standing waves for the Klein-Gordon-Maxwell system: the limit case

TL;DR

This paper proves the existence of finite energy standing wave solutions with specific phase properties for the Klein-Gordon-Maxwell system under electrostatic and large-distance gauge potential conditions.

Contribution

It establishes the existence of finite energy standing waves in the Klein-Gordon-Maxwell system with a particular phase, extending previous results to the limit case.

Findings

Existence of finite energy standing waves proven.

Solutions have phase matching the Klein-Gordon mass coefficient.

Results applicable under electrostatic and large-distance gauge potential assumptions.

Abstract

In this paper we consider the Klein-Gordon-Maxwell system in the electrostatic case, assuming the fall-off large-distance requirement on the gauge potential. We are interested in proving the existence of finite energy (and finite charge) standing waves, having the phase corresponding to the mass coefficient in the Klein-Gordon Lagrangian.