On the solutions of second order generalized 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...

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

STUDYING THE BEHAVIOR OF SOLUTIONS OF A SECOND-ORDER RATIONAL DIFFERENCE EQUATION AND A RATIONAL SYSTEM

In this paper we investigate the behavior of solutions, stable and unstable of the solutions a second-order rational difference equation. Also we will discuss about the behavior of solutions a the rational system, we show these solutions may be stable or unstable.