Existence of One Solution to a Complete Second Order Discrete Problem of Neural Type with Possibly Negative Coefficients

This paper is devoted to the study of a complete second order difference equation with possibly negative coefficients, through variational methods and critical point theory. In this case, the variational formulation is not natural, so we provide a new setting that guarantees the existence of a solution without requiring any behavior at infinity of the nonlinear term. Moreover, we present additional assumptions under which the solution turns out to be positive. Finally, we provide examples with some related numerical simulations.