Global dynamics above the ground state energy for the focusing nonlinear Klein–Gordon equation

AbstractThe analysis of global dynamics of nonlinear dispersive equations has a long history starting from small solutions. In this paper we study the focusing, cubic, nonlinear Klein–Gordon equation in R3 with large radial data in the energy space. This equation admits a unique positive stationary solution Q, called the ground state. In 1975 Payne and Sattinger showed that solutions u(t) with energy E[u,u˙] strictly below that of the ground state are divided into two classes, depending on a suitable functional K(u): If K(u)