Periodic solutions of first order linear difference equations

Homoclinic orbits for second order self-adjoint difference equations

“…A lot of attention has been devoted in recent years to find periodic solutions of discrete dynamic models, for example, see [2,[8][9][10]15]. It is our purpose in the present work to find other types of solutions, namely the doubly asymptotic solutions, first discovered by Poincaré [14] in continuous Hamiltonian systems.…”

Asymptotically periodic solutions of Volterra system of difference equations

“…A sufficient condition for the existence of a bounded solution of a class of Volterra difference equation was presented by Morchało and Szmanda in [5]. Periodic and asymptotically periodic solutions of linear difference equations were investigated, e.g., by Agarwal and Popenda in [6], and by Popenda and Schmeidel in [7,8].…”

Existence of periodic solutions of system of difference equations

“…Recently, many papers have discussed the periodic solutions of difference equations [6][7][8][9][10][11][12][13][14]. However, the periodic solutions of systems of difference equations are less studied [15'16].…”