The simplest problem lagrangian derivatives canonical variables field theory Jacobi's condition the simplest problem in parametric form problems on a conditional extremum the direct method for nonparametric problems the Sturm-Liouville problem the direct method for a problem in parametric form two-demensional problems the generalized dirichlet problem for a linear equation of elliptic type S.N.Bernshtein's principle geodesic lines on a triaxial ellipsoid Poincare's theorem on periodic extremals E.Noether's theorem on invariant functionals.
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Ахиезер et al. (1963) studied this question.