Necessary conditions for the extremum in non-smooth problems of variational calculus

Euler-Type System of Equations in Variational Problems With Delayed Argument

“…Now we assume LT y (t)− d dt LT ẏ (t) = 0, t ∈ [t 0 +h, t 0 +2h], then from ( 9)- (11), by virtue of the Lagrange lemma [7], the proof of (4) follows, i.e. part (ii) of Theorem is proven.…”

Necessary conditions for a minimum in classical calculus of variation problems in the presence of various degenerations

“…Following [3,21,22], we give a local modification of necessary condition for a minimum (1.5). Let x (•) be a weak local minimum in problem (1.1), (1.2).…”

“…Let the admissible function x (•) be an extremal in problem (1.1), (1.2) and ϑ := (θ, λ, ξ) ∈ [t 0 , t 1 )× [0, 1)× R n be an arbitrary fixed point. Consider a function of the form [22]…”