ON DISCRETE SYSTEMS WITH POTENTIAL OPERATORS

Abstract

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)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 functionalthe analogue of the Hamiltonian actionis presented. The illustrative example is given.