Abstract
Conditions for the solvability of the problem inverse to the linear autonomous Noether boundary-value problem for the system of ordinary differential equations have been found.
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References
A. A. Boichuk, “The Green function of the linear homogeneous boundary-value problem,” Dokl. Acad. Nauk UkrSSR Ser A, 7, 2–6 (1988).
A. A. Boichuk and A. M. Samoilenko, Generalized Inverse Operators and Fredholm Boundary-Value Problems; 2nd Edition. Berlin, Boston, De Gruyter (2016).
A. A. Samarskii and P. N. Vabyshchevich, Numerical Methods for Solving Inverse Problems of Mathematical Physics. M., Izd. LKI (2009).
F. Natterer, Mathematical Aspects of Computer Tomography. M., Mir (1990).
P. S. Stanimirovic, I. Stojanovic, D. Pappas, and S. Chountasis, “On removing blur in images using least squares solutions,” Philomat, 30(14), 3855–3866 (2016).
A. N. Tikhonov and V. Ya. Arsenin, Methods for Solving Ill-Posed Problems, M., Nauka (1986).
N. I. Akhiezer, Lectures on the Approximation Theory, M., Nauka (1965).
S. M. Chuiko, “On approximate solution of boundary value problems by the least square method,” Nonlinear Oscillations (N.Y.), 11(4), 585–604 (2008).
J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd Edition, Wiley (1999).
S. M. Chuiko, “A generalized matrix differential-algebraic equation,” Journal of Mathematical Sciences 210(1), 9–21 (2015).
V. V. Voevodin and Yu. A. Kuznetsov, Matrices and Calculations, M., Nauka (1984).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, M., Nauka (1968).
A. A. Boichuk, Constructive Methods for the Analysis of Boundary-Value Problems, Kyiv, Naukova Dumka (1990).
A. A. Boichuk and S. A. Krivosheya, “A Critical periodic boundary value problem for a matrix Riccati equation,” Differential Equations, 37(4), 464–471 (2001).
S. M. Chuiko, “Generalized Green Operator of Noetherian boundary-value problem for matrix differential equation,” Russian Mathematics, 60(8), 64–73 (2016).
R. Bellman, Introduction to Matrix Theory, M., Nauka (1969).
S. M. Chuiko, O. V. Nesmelova, and Y. V. Kalinichenko, “Conditions for the solvability of the problem inverse to the Cauchy problem for the difference-algebraic equation,” Nonlinear Oscillations, 24(3), 422– 434 (2021).
V. Ya. Gutlyanskii, O. V. Nesmelova, and V. I. Ryazanov, “The Dirichlet problem for the Poisson type equations in the plane,” Dopov. Nats. Akad. Nauk Ukr., 5, 10–16 (2020).
I. I. Skrypnik, “Removeability of isolated singularities for anisotropic elliptic equations with gradient absorption,” Israel Journal of Mathematics, 215(1), 163–179 (2016).
S. L. Campbell, Singular Systems of differential equations. San Francisco–London–Melbourne, Pitman Advanced Publishing Program (1980).
S. M. Chuiko, “On a reduction of the order in a differential-algebraic system,” Journal of Mathematical Sciences, 235(1), 2–14 (2018).
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Translated from Ukrains’ki˘ı Matematychny˘ı Visnyk, Vol. 19, No. 3, pp. 315–326, July–September, 2022.
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Chuiko, S.M. Conditions for the Solvability of the Problem Inverse to the Linear Autonomous Noether Boundary-Value Problem. J Math Sci 268, 147–156 (2022). https://doi.org/10.1007/s10958-022-06188-x
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DOI: https://doi.org/10.1007/s10958-022-06188-x