Localised time-periodic solutions of discrete nonlinear Klein–Gordon systems with convex on-site potentials

The existence of nonzero localised periodic solutions for general one-dimensional discrete nonlinear Klein-Gordon systems with convex on-site potentials is proved. The existence problem of localised solutions is expressed in terms of a fixed point equation for an operator on some appropriate function space which is solved by means of Schauder's Fixed Point Theorem.