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Sib. Èlektron. Mat. Izv., 2016, Volume 13, Pages 452–466 (Mi semr689)  

Differentical equations, dynamical systems and optimal control

Nonlocal problems with an integral boundary condition for the differential equations of odd order

A. I. Kozhanovab, G. A. Lukinac

a Novosibirsk State University, ul. Pirogova, 2, 630090, Novosibirsk, Russia
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
c Mirny Polytechnic Institute (branch) of Ammosov North-Eastern Federal University, ul. Tikhonova, 5 korp. 1, 678170, Mirny, Russia

Abstract: We study the solvability of nonlocal problems for equations
$$u_{ttt} + Au=f(x,t)$$
($0<T<+\infty$, $A$ — elliptic operator) with only two boundary conditions instead of three and with a special integral boundary condition. We prove the existence theorems for regular solutions and indicate a possible generalization of the obtained results.

Keywords: nonlocal problem, integral condition, odd order differential equation, regular solution, existence.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-06582_


DOI: https://doi.org/10.17377/semi.2016.13.039

Full text: PDF file (188 kB)
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Bibliographic databases:

UDC: 517.946
MSC: 35N99,35R99
Received February 22, 2016, published June 1, 2016

Citation: A. I. Kozhanov, G. A. Lukina, “Nonlocal problems with an integral boundary condition for the differential equations of odd order”, Sib. Èlektron. Mat. Izv., 13 (2016), 452–466

Citation in format AMSBIB
\Bibitem{KozLuk16}
\by A.~I.~Kozhanov, G.~A.~Lukina
\paper Nonlocal problems with an integral boundary condition for the differential equations of odd order
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 452--466
\mathnet{http://mi.mathnet.ru/semr689}
\crossref{https://doi.org/10.17377/semi.2016.13.039}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3512694}


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