## Periodic solutions for discrete convex Hamiltonian systems via Clarke duality.(English)Zbl 1121.39012

Applying Clarke duality and the perturbation technique, the authors prove the existence of a periodic solution for a certain class of periodic Hamiltonian systems, namely: $J\Delta u(n)+\nabla H(n, Lu(n))= f(n),$ where $u(n)= \begin{pmatrix} u_1(n)\\ u_2(n)\end{pmatrix},\quad Lu(n)= \begin{pmatrix} u_1(n+1)\\ u_2(n)\end{pmatrix},\quad f(n)= \begin{pmatrix} f_1(n)\\ f_2(n)\end{pmatrix}$ are in $$\mathbb{R}^{2N}$$ with $$N$$ a given positive integer, $$\Delta u(n)= u(n+ 1)- u(n)$$ and $$u(n+ T)= u(n)$$ for $$n\in\mathbb{Z}$$ and $$T$$ a fixed positive integer.

### MSC:

 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis
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