×

zbMATH — the first resource for mathematics

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)
PDF BibTeX XML Cite
Full Text: EMIS EuDML