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.

中文翻译：

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具有凸形现场势的离散非线性Klein-Gordon系统的局部时间周期解

证明了具有凸形现场势的一维离散非线性Klein-Gordon系统的非零局部周期解的存在。局部解的存在问题用算子在某个适当的函数空间上的不动点方程表示，该空间通过Schauder不动点定理来求解。