Existence of exponentially spatially localised breather solutions for lattices of nonlinearly coupled particles: Schauder's fixed point approach.

We prove the existence of exponentially localised breather solutions for lattices of coupled particles with nonlinear nearest neighbour interaction. The second derivative of the associated interaction potentials is bounded by a power-law growth. The existence problem is formulated in terms of a fixed point equation considered in weighted sequence spaces, which is solved by means of Schauder's Fixed Point Theorem.