Existence theorems of periodic solutions for second-order difference equations containing both advance and retardation

Existence and multiple solutions for second-order p-Laplacian difference equations

“…In this paper, we investigate the solutions of boundary value problems (1.1) with (1.2) for a second-order p-Laplacian difference equation [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. By using the critical point theory [26][27][28], the existence and multiple results are obtained.…”

Existence of homoclinic orbits for a higher order difference system

“…containing both advance and retardation [27] by using the mountain pass lemma in combination with periodic approximations. Recently, Shi et al [22] studied the existence of a nontrivial homoclinic orbit for second order pLaplacian difference equations containing both advance and retardation…”