Singular discrete problem arising in the theory of shallow membrane caps

On four types of solutions of a second-order difference equation

“…By Lemma 4.3, the sequence {y ½h n } 1 n¼0 , P a contains a subsequence which is uniformly converging on ½0; a. Using the same arguments as in [19], we get that the limit function is a solution of problem (4.17). (Other arguments giving this result can also be found in [8] or [10].)…”

“…Note that an autonomous case of (2.1) was studied in [16]. We also mention also some recent works investigating the solvability of other secondorder discrete boundary value problems, for example [1], [2], [7], [11], [15], [19], [20], [22].…”

Homoclinic solutions of non-autonomous difference equations arising in hydrodynamics

“…Note that an autonomous case of (2.1) was studied in [9]. We mention also some recent papers investigating the solvability of other second-order discrete boundary value problems, for example [10][11][12][13][14][15][16].…”

Reverse-Order Lower and Upper Functions for Periodic Problems of Second-Order Singular Difference Equations

“…Recently, there are many papers to study the existence of positive periodic solutions for second-order difference equations, see [2][3][4][5][6][7] and their references therein. However, there are few techniques for studying the existence of positive solutions of difference equations with singularity, and thus the results in the field are very rare, see [8][9][10][11][12][13]. The existence of positive periodic solutions for continuous case has been studied by Torres, see [14,15].…”