On the Solutions of Fourth Order Difference Equations

New oscillation criteria for third order nonlinear neutral difference equations

“…For contributions, for third order difference equations, we refer the reader to the papers [2,5,7,8,11,12,13,15,16,17,18,19] and for neutral difference equations we refer the reader to the papers [14,20] and the references cited therein. For completeness and comparison, we present below some of these results.…”

Existence of periodic solutions of fourth-order nonlinear difference equations

“…Particularly, Guo and Yu [16][17][18] and Shi et al [30] studied the existence of periodic solutions of second-order nonlinear difference equations by using the critical point theory. Compared to one-order or second-order difference equations, the study of higher-order equations, and in particular, fourth-order equations, has received considerably less attention(see, for example, [1,7,10,14,21,27,28,32,34] and the references contained therein). However, to the best of our knowledge, results obtained in the literature on the periodic solutions of (1.1) are very scarce.…”

Existence of solutions of nonlinear fourth order discrete boundary value problem

“…Difference equation (1.1) was studied by Popenda and Schmeidel [6] and Taylor [7] with p n ; 1. Peil and Peterson [5] studied equation (1.1) as a linear equation with f ðn; x n Þ ¼ 2r n x n .…”