Geodesic
Inverse Problem of the Variational Calculus for Differential Equations of Second Order with Deviating Argument
Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 231-241

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We obtain conditions for the solvability of the inverse problem of the variational calculus for differential equations of second order with deviating argument of special form as well as the formula for the functional of the inverse problem defined by the integral that differs from the standard one by that the required function has a retarded argument.
Keywords: differential equation of second order with deviating argument, inverse problem of the variational calculus, function with retarded argument, Pontryagin's maximum principle, the spaces $W^1_2$.
Mots-clés : Euler's equation 
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     author = {V. G. Zadorozhniy and G. A. Kurina},
     title = {Inverse {Problem} of the {Variational} {Calculus} for {Differential} {Equations} of {Second} {Order} with {Deviating} {Argument}},
     journal = {Matemati\v{c}eskie zametki},
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V. G. Zadorozhniy; G. A. Kurina. Inverse Problem of the Variational Calculus for Differential Equations of Second Order with Deviating Argument. Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 231-241. http://geodesic.mathdoc.fr/item/MZM_2011_90_2_a5/