The (2,2)-disconjugacy of a fourth order difference equation

On the nonexistence and existence of solutions for a fourth-order discrete Dirichlet boundary value problem

“…We also refer to [46,47] for the discrete boundary value problems. 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, [2,11,12,15,31,32,34,35,38,42,44] and the references contained therein). Yan, Liu [44] in 1997 and Thandapani, Arockiasamy [42] in 2001 studied the following fourth-order difference equation of form,…”

Nonexistence and Existence Results for a Fourth-Order p-Laplacian Discrete Neumann Boundary Value Problem

“…In 1995, Peterson and Ridenhour considered the disconjugacy of equation (1.7) when γ n ≡ 1 and f (n, u n ) = q n u n (see [38]). The boundary value problem (BVP) for determining the existence of solutions of difference equations has been a very active area of research in the last twenty years, and for surveys of recent results, we refer the reader to the monographs by Agarwal et al [2,16,30,36,40].…”

“…We also refer to [47,48] for the discrete boundary value problems. Compared to firstorder 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, [10][11][12][13][14]17,18,[28][29][30][31]34,38,43,45] and the references contained therein). Yan and Liu [45] and Thandapani and Arockiasamy [43] studied the following fourthorder difference equation of form,…”

Existence of periodic solutions of fourth-order nonlinear difference equations

“…In 1995, Peterson and Ridenhour [27] considered the disconjugacy of the following equation Furthermore, [7] is the only paper we found which deals with the problem of periodic solutions to fourth-order difference Eq. (1.5).…”

“…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.…”