In this article,we present some new sufficient conditions for the oscillation of all solutions of a second order difference equation with several super-linear neutral terms. The results obtained here extend or complement some of the known results reported in the literature. Examples illustrating the importance of the main results are included.

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Artificial neural networks have been developed as generalizations of mathematical models of biological nervous system. In this paper we investigate periodicity of neutral typed delay difference equations of unbounded activation functions via fixed point theory and some new techniques; various sufficient conditions for the existence of positive periodic solutions are established.