Factoring of second-order difference equations with periodic coefficients.

Periodic Solutions of Second Order Nonlinear Functional Difference Equations

The development of the study of periodic solution of functional difference equations is relatively rapid. There has been many approaches to study periodic solutions of difference equations, such as critical point theory, fixed point theorems in Banach spaces or in cones of Banach spaces, coincidence degree theory, KaplanYorke method, and so on, one may see [3-7,11,13-15] and the references ther...

Periodic solutions for nonlinear second-order difference equations

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 ifN is an odd integer...

Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations

Critical Oscillation Constant for Difference Equations with Almost Periodic Coefficients

and Applied Analysis 3 is conditionally oscillatory with the oscillation constant K 1/4. It is known see 22 that the equation [ r t y′ t ]′ γs t t2 y t 0, 1.5 where r, s are positive periodic continuous functions, is conditionally oscillatory as well. We also refer to 23 and 24–29 which generalize 23 for the discrete case, see 30 . Since the Euler difference equation Δyk γ k 1 k yk 1 0 1.6 is c...

Oscillation of a Class of Nonlinear Difference Equations of Second Order with Oscillating Coefficients

In this paper, we study asymptotic behaviour of solutions of the following second-order difference equation: ∆ [ a(n)∆ [ x(n)+r(n)F (x(n−ρ)) ]] +p(n)G (x(n− τ))−q(n)G (x(n− σ)) = s(n), where n ∈ N0 := N ∪ {0}, {r(n)}n∈N0 and {s(n)}n∈N0 are sequences of real numbers, {p(n)}n∈N0 and {q(n)}n∈N0 are nonnegative sequences of real numbers, {a(n)}n∈N0 is positive, ρ, τ, σ ≥ 0 are integers and F,G are ...