On a class of nonlinear difference equations

On the Existence and the Asymptotic Behavior of Nonoscillatory Solutions of Second Order Quasilinear Difference Equations

“…To prove our main results, we use, beside properties of normalized regularly varying sequence, the next two results: the discrete analog of the Lebesgue dominated convergence theorem and the fixed point theorem, which was proved in [22] and which can be considered as a discrete analog of Schauder's fixed point theorem.…”

Asymptotic behavior of positive solutions of fourth-order nonlinear difference equations

“…Compared to second-order difference equations, the study of higher-order equations (see [3][4][5][6][7][8]) and, in particular, fourth-order difference equations (see [9][10][11][12][13][14]) has received considerably less attention.…”

A classification scheme for nonoscilatory solutions of a higher order neutral nonlinear difference equation

“…We then change the definition of F(n) to V(n) = 1 for n > 0. [14], only results related to fourth order equations are discussed.…”

“…have been studied by a number of people (see [12][13][14]) and several results are related to classifications of nonoscillatory solutions. Other related results can be found in [1][2][3][4][5][7][8][9][10][11][12][13][14][15][16].…”