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Mat. Zametki, 2011, Volume 90, Issue 2, Pages 231–241 (Mi mz8709)  

Inverse Problem of the Variational Calculus for Differential Equations of Second Order with Deviating Argument

V. G. Zadorozhniya, G. A. Kurinab

a Voronezh State University
b Voronezh State Academy of Forestry Engineering

Abstract: 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, Euler's equation, Pontryagin's maximum principle, the spaces $W^1_2$

DOI: https://doi.org/10.4213/mzm8709

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English version:
Mathematical Notes, 2011, 90:2, 218–226

Bibliographic databases:

UDC: 517.972.7+517.929
Received: 20.11.2009

Citation: V. G. Zadorozhniy, G. A. Kurina, “Inverse Problem of the Variational Calculus for Differential Equations of Second Order with Deviating Argument”, Mat. Zametki, 90:2 (2011), 231–241; Math. Notes, 90:2 (2011), 218–226

Citation in format AMSBIB
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