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A class of difference equations which include discrete nonlinear Schrödingerequations as special cases are considered. New sufficient conditions of the existenceand multiplicity results of homoclinic solutions for the difference equations are obtainedby making use of the mountain pass theorem and the fountain theorem, respectively. Recent results in the literature are generalized and greatly improved

Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials