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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2020, Volume 24, Number 4, Pages 607–620
DOI: https://doi.org/10.14498/vsgtu1821 (Mi vsgtu1821) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differential Equations and Mathematical Physics

Non-local problems with an integral condition for third-order differential equations

A. I. Kozhanova, A. V. Dyuzhevab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation
b Samara State Technical University, Samara, 443100, Russian Federation
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DOI: https://doi.org/10.14498/vsgtu1821
Abstract: The paper is devoted to the study of the solvability of nonlocal problems with an integral variable $t$ condition for the equations
$$u_{tt}+\left(\alpha\frac{\partial}{\partial t}+\beta\right)\Delta u=f(x,t)$$
($\alpha$, $\beta$ are valid constants, $\Delta$ is Laplace operator by spatial variables). Theorems are proved for the studied problems existence and non-existence, uniqueness and non-uniqueness solutions (having all derivatives generalized by S. L. Sobolev included in the equation).
Keywords: third-order differential equations, non-local problems, integral conditions, regular solutions, uniqueness, existence.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 0778-2020-0005
The work was carried out with the financial support of the Ministry of education and science of the Russian Federation in the framework of state task, no. 0778–2020–0005.
Received: August 21, 2020
Revised: October 17, 2020
Accepted: November 16, 2020
First online: November 30, 2020
Bibliographic databases:
Document Type: Article
UDC: 517.953
MSC: 35M10
Language: Russian
Citation: A. I. Kozhanov, A. V. Dyuzheva, “Non-local problems with an integral condition for third-order differential equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 24:4 (2020), 607–620
Citation in format AMSBIB
\Bibitem{KozDyu20}
\by A.~I.~Kozhanov, A.~V.~Dyuzheva
\paper Non-local problems with an integral condition for~third-order differential equations
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2020
\vol 24
\issue 4
\pages 607--620
\mathnet{http://mi.mathnet.ru/vsgtu1821}
\crossref{https://doi.org/10.14498/vsgtu1821}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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