The theorem of the resolution of the inverse problem of variation calculus for the ordinary differential equations of the sixth order

S. Kobzistyy; N. Andreeva; E. Korchagina; V. Korchagin

doi:10.12737/5122

THE THEOREM OF THE RESOLUTION OF THE INVERSE PROBLEM OF VARIATION CALCULUS FOR THE ORDINARY DIFFERENTIAL EQUATIONS OF THE SIXTH ORDER The theorem of the resolution of the inverse problem of variation calculus for the ordinary differential equations of the sixth order

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Published in Actual directions of scientific researches of the XXI century: theory and practice · Volume 2, Issue 4, p. 2 · Pages 90–0 · Rubric: Section: Differential and Integral Equations

DOI: https://doi.org/10.12737/5122

Received: 29.08.2014 Accepted: 03.10.2014 Published: 03.10.2014 Language of publication: RUS

Authors

S. Kobzistyy

N. Andreeva

E. Korchagina

V. Korchagin

S. Kobzistyy

N. Andreeva

E. Korchagina

V. Korchagin

ABSTRACT

Necessary and sufficient conditions are obtained for the solvability of the inverse problem of the calculus of variations for ordinary differential equation of the sixth order. As a consequence of this result, we obtain necessary and sufficient conditions for the solvability of inverse problems of the variation calculus for the ordinary differential equations of the fourth and the second order, considered in [1].

KEYWORDS

the differential equations, the inverse problem of variation calculus, functional, Frechet differential

1. Zadorozhniy V. G. Differentsial´nye uravneniya s variatsionnymi proizvodnymi. Voronezh, VorGU, 2000.

2. Zadorozhniy V. G., Korchagina E. V. Usloviya razreshimosti obratnoy zadachi variatsionnogo ischisleniya dlya obyknovennogo differentsial´nogo uravneniya shestogo poryadka. Trudy molodykh uchenykh 2/2000, VGU, 2001. -s.48-61

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GOST

Kobzistyy S., Andreeva N., Korchagina E., Korchagin V. The theorem of the resolution of the inverse problem of variation calculus for the ordinary differential equations of the sixth order // Actual directions of scientific researches of the XXI century: theory and practice. 2014. no. 4. pp. 90-0. DOI: https://doi.org/10.12737/5122. (Date of access 18.10.2026).

MLA

S. Kobzistyy, Andreeva N., Korchagina E., Korchagin V.. "The theorem of the resolution of the inverse problem of variation calculus for the ordinary differential equations of the sixth order." Actual directions of scientific researches of the XXI century: theory and practice 2.4 (2014): 90-0. DOI: https://doi.org/10.12737/5122.

APA

Kobzistyy S., Andreeva N., Korchagina E., Korchagin V. (2014). The theorem of the resolution of the inverse problem of variation calculus for the ordinary differential equations of the sixth order. Actual directions of scientific researches of the XXI century: theory and practice, 2(4), 90-0. https://doi.org/10.12737/5122

Chicago

S. Kobzistyy, Andreeva N., Korchagina E., Korchagin V.. "The theorem of the resolution of the inverse problem of variation calculus for the ordinary differential equations of the sixth order." Actual directions of scientific researches of the XXI century: theory and practice 2, no. 4 (2014): 90-0. https://doi.org/10.12737/5122.

WIKI

{{cite journal | author = Kobzistyy S., Andreeva N., Korchagina E., Korchagin V. | title = The theorem of the resolution of the inverse problem of variation calculus for the ordinary differential equations of the sixth order | journal = Actual directions of scientific researches of the XXI century: theory and practice | year = 2014 | volume = 2 | issue = 4 | pages = 90-0 | doi = 10.12737/5122 }}

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THE THEOREM OF THE RESOLUTION OF THE INVERSE PROBLEM OF VARIATION CALCULUS FOR THE ORDINARY DIFFERENTIAL EQUATIONS OF THE SIXTH ORDER The theorem of the resolution of the inverse problem of variation calculus for the ordinary differential equations of the sixth order

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