On discrete systems with potential operators

The main purpose of this work is to study the potentiality of a discrete system obtained from the system of the form $C(t, u)\dot u (t) + E(t, u) = 0$ with continuous time. The definition of potentiality of the corresponding discrete system is introduced. Necessary and sufficient conditions for its potentiality with respect to a given bilinear form are obtained. The algorithm for the construction of the corresponding functional—the analogue of the Hamiltonian action—is presented. The illustrative example is given.