RUSSIA

There is considered the problem of extremum of the nonlocal functional

where s₁ - s₀ > r₁+r₂ , r₁ , r ₂ are some integers and u— (t,s): = u(t,s)/ t.

There are derived for this problem the second variation of a functional, the generalized necessary condition of Legendre and the generalized Lagrange theorem concerning the conditional extremum of nonlocal functionals.