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Periodic solutions of nonlinear second-order difference equations
Advances in Difference Equations volume 2005, Article number: 718682 (2005)
We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by (t + 1) + cy(t) = f (y(t)), where f: ℝ → ℝ and β > 0 is continuous. In our main result we assume that f exhibits sublinear growth and that there is a constant uf (u) > 0 such that |u| ≥ β whenever c = 1. For such an equation we prove that if N is an odd integer larger than one, then there exists at least one N-periodic solution unless all of the following conditions are simultaneously satisfied: |b| < 2, N across-1(-b/2), and π is an even multiple of c ≠ 0.
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Rodriguez, J., Etheridge, D.L. Periodic solutions of nonlinear second-order difference equations. Adv Differ Equ 2005, 718682 (2005). https://doi.org/10.1155/ADE.2005.173