Periodic solutions of higher-dimensional discrete systems. (English) Zbl 1073.39010

The authors consider the second-order discrete system \[ \Delta^2X_{n-1}+ f(n, X_n)= 0,\quad n\in\mathbb{Z},\tag{1} \] where \(f\in C(\mathbb{R}\times \mathbb{R}^m, \mathbb{R}^m)\), \(f(t+ M,\mathbb{Z})= f(t,\mathbb{Z})\) for any \((t,\mathbb{Z})\in \mathbb{R}\times \mathbb{R}^m\) and \(M\) is a positive integer. The existence of \(M\) periodic solutions of (1) is proved.


39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
34C25 Periodic solutions to ordinary differential equations
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