Existence of hylomorphic solitary waves in Klein–Gordon and in Klein–Gordon–Maxwell equations

Abstract

This paper is devoted to the study of solitary waves whose existence is related to the ratio energy/charge. These solitary waves are called hylomorphic. This class includes the Q-balls, which are spherically symmetric solutions of the nonlinear Klein–Gordon equation (NKG), as well as solitary waves and vortices which occur, by the same mechanism, in the nonlinear Schrödinger equation and in gauge theories. It is proved an abstract theorem which allows to show the existence of hylomorphic solitary waves and vortices in the (NKG) and in the nonlinear Klein–Gordon–Maxwell equations (NKGM).