## On periodic motions of lattices of Toda type via critical point theory.(English)Zbl 0809.34056

The ordinary differential systems of Toda type are studied, in which the potential of the interaction between the $$n$$th and the $$(n+1)$$st particle is superquadratic at $$-\infty$$ and has weaker growth at $$+\infty$$. Under fixed end points condition as well as the identified end points condition, the authors prove that there exist infinitely many $$T$$- periodic solutions for every $$T>0$$. The global variational method and the relative $$S^ 1$$-index theory are used.

### MSC:

 34C25 Periodic solutions to ordinary differential equations 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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### References:

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