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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.

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