Inverse problem of the calculus of variations for systems of differential-difference equations of second order. (English. Russian original) Zbl 1035.49033

Popov, A. M.

Math. Notes 72, No. 5, 687-691 (2002); translation from Mat. Zametki 72, No. 5, 745-749 (2002).

Summary: The inverse problem of the calculus of variations for second-order nonlinear and linear systems of differential-difference equations is considered. The relationship between the formal potentiality of a linear system with constant coefficients and the eveness of its characteristic function is established.

MSC:

49N45	Inverse problems in optimal control
34K29	Inverse problems for functional-differential equations

Keywords:

potential operators; Helmholtz potentiality conditions; inverse problem; differential-difference equations