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Multiple and particular solutions of a second order discrete boundary value problem with mixed periodic boundary conditions

. In this paper, a second order discrete boundary value problem with a pair of mixed periodic boundary conditions is considered. Sufﬁcient conditions on the existence of multiple solutions are obtained by using the critical point theory. Necessary conditions for a particular solution subject to pre-deﬁned criteria are also investigated. Examples are given to illustrate the applications of the results as well.