Sum of two dimensional Fibonacci sequence by solutions of second order difference equations

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...

Bounded Solutions to Nonhomogeneous Linear Second-Order Difference Equations

By using some solvability methods and the contraction mapping principle are investigated bounded, as well as periodic solutions to some classes of nonhomogeneous linear second-order difference equations on domains N0, Z \N2 and Z. The case when the coefficients of the equation are constant and the zeros of the characteristic polynomial associated to the corresponding homogeneous equation do not...

Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations

For nonnegative real numbers α, β, γ , A, B, and C such that B C > 0 and α β γ > 0, the difference equation xn 1 α βxn γxn−1 / A Bxn Cxn−1 , n 0, 1, 2, . . . has a unique positive equilibrium. A proof is given here for the following statements: 1 For every choice of positive parameters α, β, γ , A, B, and C, all solutions to the difference equation xn 1 α βxn γxn−1 / A Bxn Cxn−1 , n 0, 1, 2, . ...

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