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Periodic solutions of second order nonlinear functional difference equations. (English) Zbl 1164.39005
Sufficient conditions for the existence of at least one $$T$$-periodic ($$T\in \mathbb T$$) solution of the second order difference equation $\Delta ^2 x(n-1)=f(n,x(n),x(n-\tau _1(n)),\dots , x(n-\tau _m(n))), \quad n\in \mathbb Z, \tag{$$*$$}$ are presented. It is supposed that the function $$f$$ and the delays $$\tau _i\:\mathbb N\to \mathbb N$$ are $$T$$-periodic in $$n$$. The sufficient conditions are formulated in terms of growth restrictions on the nonlinearity $$f$$. The main method used in the proofs is the coincidence degree theory applied to a certain operator associated with ($$*$$).

##### MSC:
 39A11 Stability of difference equations (MSC2000)
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