On variational methods for periodic discrete problems

Dependence on parameters for a discrete Emden–Fowler equation

“…Next, let us take a sequence {u n } ∞ n=1 ⊂ X converging to some u ∈ X and let {x n } ∞ n=1 be a sequence of solutions to (14) corresponding to the relevant elements of the sequence {u n } ∞ n=1 . By (13) and by (15) we see that for all n ∈ N we have…”

Multiplicity results for nonlinear periodic fourth order difference equations with parameter dependence and singularities

“…The employed tools are, among others, the method of upper and lower solutions [3][4][5]11,15,16,23,24], monotone iterative techniques [9,10,27,28] or variational methods [2,13,25,26]. The dependence on a real parameter has been recently considered for p-Laplacian equations in [8,12].…”

On variational methods for nonlinear difference equations

“…In some cases the multiplicity is also considered. To mention a few papers [1][2][3][4], see also for example, [5,6,1,7]. Mainly the mountain pass methodology is applied, the linking theorem is involved and the Palais-Smale type condition is assumed.…”