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Journal of the Belarusian State University. Mathematics and Informatics, 2018, Volume 1, Pages 17–28 (Mi bgumi126)  

Differential equations and Optimal control

Boundary value problem for system of finite-difference with averaging equations

S. A. Spaskova, Khmyzov Anton K.b

a Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
b Epam Systems, 1/1 Akademika Kupreviča Street, Minsk 220141, Belarus
References:
Abstract: The boundary value problem for the system of linear nonhomogeneous differential equations with generalized coefficients is considered
$$ \begin{cases} \dot{X}(t)=\dot{L}(t)X(t)+\dot{F}(t), \\ M_{1}X(0)+M_{2}X(b)=Q, \end{cases} $$
where $t\in T=[0,b], L:T\rightarrow \mathbb{R}^{p\times p}$ и $F:T\rightarrow \mathbb{R}^{p}$ are right-continuous matrix and vector valued functions of bounded variation; $M_{1}, M_{2}\in \mathbb{R}^{p\times p}, Q\in \mathbb{R}^{p}$ are defined matrices and vector. The problem is investigated with the help of the corresponding finite-difference with averaging equation behavior studying. The definition of the fundamental matrix, corresponding to the finite-difference with averaging equation is introduced. The theorem of the existence and uniqueness of the finite-difference with averaging boundary value problem, corresponding to the described system is proved.
Keywords: system of linear nonhomogeneous differential equations; boundary value problem; finite-difference with averaging equations; fundamental matrix.
Received: 04.09.2017
Document Type: Article
UDC: 517.9
Language: Russian
Citation: S. A. Spaskov, Khmyzov Anton K., “Boundary value problem for system of finite-difference with averaging equations”, Journal of the Belarusian State University. Mathematics and Informatics, 1 (2018), 17–28
Citation in format AMSBIB
\Bibitem{SpaKhm18}
\by S.~A.~Spaskov, Khmyzov Anton K.
\paper Boundary value problem for system of finite-difference with averaging equations
\jour Journal of the Belarusian State University. Mathematics and Informatics
\yr 2018
\vol 1
\pages 17--28
\mathnet{http://mi.mathnet.ru/bgumi126}
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