Báo Cáo Báo cáo hóa học NONLINEAR SECOND-ORDER DIFFERENCE EQUATIONS JESUS RODRIGUEZ AND DEBRA LYNN

PERIODIC SOLUTIONS OF NONLINEAR SECOND-ORDER DIFFERENCE EQUATIONS ´ JESUS RODRIGUEZ AND DEBRA LYNN ETHERIDGE Received 6 August 2004

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 c = 0 and f : R → R is continuous.

In our main result we assume that f exhibits sublinear growth and that there is a constant β 0 such that u f (u) 0 whenever |u| ≥ β. 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: c = 1, |b|