A multiplicity result for the nonlinear Klein Gordon Maxwell equations

TL;DR

This paper introduces a new iterative technique to find multiple solutions for the nonlinear Klein-Gordon-Maxwell equations, improving upon previous methods and applicable in physically relevant scenarios.

Contribution

The authors develop a novel iterative approach that enhances existing reduction methods, enabling the demonstration of multiple solutions in the positive potential case.

Findings

Established a new iterative method for Klein-Gordon-Maxwell equations

Achieved multiplicity results in the positive potential context

Improved solution-finding techniques over previous reduction methods

Abstract

In this paper we provide a new technique to find solutions to the Klein-Gordon-Maxwell system. The method, based on an iterative argument, permits to improve previous results where the reduction method was used. We also show how this device permits to obtain a multiplicity result in the physically significant context known as "the positive potential case".