Existence of periodic and subharmonic solutions for second-order superlinear difference equations

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Subharmonic Solutions with Prescribed Minimal Period of a Discrete Forced Pendulum Equation (2004, background): “However, there are scarce techniques for studying the existence of periodic solutions of discrete systems, results in this field are very rare (see [1, 10 ,11,21]).”
Periodic Solutions of Second Order Self‐Adjoint Difference Equations (2005, background): “1) was discussed in two recent papers [15, 16].”
Existence of Periodic and Subharmonic Solutions for Second-Order p-Laplacian Difference Equations (2007, methodology): “1), we will state some basic notations and lemmas (see [5, 8]), which will be used in the proofs of our main results.”
Boundary value problems of discrete generalized Emden-Fowler equation (2006, unknown): “[14,15,18,19,21,22,27–29]. In two recent papers [ 16 ,17] , the authors”