×

Inverse problem of the variational calculus for differential equations of second order with deviating argument. (English. Russian original) Zbl 1237.49052

Math. Notes 90, No. 2, 218-226 (2011); translation from Mat. Zametki 90, No. 2, 231-241 (2011).
Summary: 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.

MSC:

49N45 Inverse problems in optimal control
49J15 Existence theories for optimal control problems involving ordinary differential equations
34K29 Inverse problems for functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] V. G. Zadorozhnii, Methods of Variational Analysis (IKI, Moscow-Izhevsk, 2006) [in Russian].
[2] L. É. Él’sgol’ts and S. B. Norkin, Introduction to the Theory of Differential Equations with Deviating Argument (Nauka, Moscow, 1971) [in Russian].
[3] L. É. Él’sgol’ts, Qualitative Methods in Mathematical Analysis (Gostekhizdat, Moscow, 1955) [in Russian].
[4] G. Kamenskii, ”On boundary value problems connected with variational problems for nonlocal functionals,” Funct. Differ. Equ. 12(3–4), 245–270 (2005). · Zbl 1086.34057
[5] G. A. Kamenskii, ”Asymmetrical variational problems for functionals with deviating argument,” Ukrain.Mat. Zh. 41(5), 602–609 (1989) [UkrainianMath. J. 41 (5), 521–527 (1989)]. · Zbl 0715.49009 · doi:10.1007/BF01060536
[6] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, 3d ed. (Nauka, Moscow, 1976) [in Russian].
[7] L. S. Gnoenskii, G. A. Kamenskii, and L. É. Él’sgol’ts, Mathematical Foundations of the Theory of Control Systems (Nauka, Moscow, 1969) [in Russian].
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.