Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance

Research Article Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance

On a System of Second-Order Nonlinear Difference Equations

This paper is concerned with dynamics of the solution to the system of two second-order nonlinear difference equations 1 1 1 n n n n x x A x y + − − = + , 1 1 1 n n n n y y A x y + − − = + ,  n = 0,1, , where ( ) 0, A∈ ∞ , ( ) 0, i x− ∈ ∞ , ( ) 0, i y− ∈ ∞ , i = 0, 1. Moreover, the rate of convergence of a solution that converges to the equilibrium of the system is discussed. Finally, some num...

Oscillation of second order nonlinear neutral delay difference equations

In this paper sufficient conditions are obtained for oscillation of all solutions of a class of nonlinear neutral delay difference equations of the form ∆(y(n) + p(n)y(n−m)) + q(n)G(y(n − k)) = 0 under various ranges of p(n). The nonlinear function G,G ∈ C(R,R) is either sublinear or superlinear. Mathematics Subject classification (2000): 39 A 10, 39 A 12

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...

Homoclinic Orbits of Second-order Nonlinear Difference Equations

We establish existence criteria for homoclinic orbits of secondorder nonlinear difference equations by using the critical point theory in combination with periodic approximations.