# On the two-point boundary-value problem for the Riccati matrix differential equation

Open Mathematics (2005)

- Volume: 3, Issue: 1, page 143-154
- ISSN: 2391-5455

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topV. Laptinsky, and I. Makovetsky. "On the two-point boundary-value problem for the Riccati matrix differential equation." Open Mathematics 3.1 (2005): 143-154. <http://eudml.org/doc/268790>.

@article{V2005,

abstract = {Constructive sufficient conditions for univalent resolvability of a two-point boundary value problem for nonlinear Riccati equation are obtained. An illustrative example is given.},

author = {V. Laptinsky, I. Makovetsky},

journal = {Open Mathematics},

keywords = {34B10},

language = {eng},

number = {1},

pages = {143-154},

title = {On the two-point boundary-value problem for the Riccati matrix differential equation},

url = {http://eudml.org/doc/268790},

volume = {3},

year = {2005},

}

TY - JOUR

AU - V. Laptinsky

AU - I. Makovetsky

TI - On the two-point boundary-value problem for the Riccati matrix differential equation

JO - Open Mathematics

PY - 2005

VL - 3

IS - 1

SP - 143

EP - 154

AB - Constructive sufficient conditions for univalent resolvability of a two-point boundary value problem for nonlinear Riccati equation are obtained. An illustrative example is given.

LA - eng

KW - 34B10

UR - http://eudml.org/doc/268790

ER -

## References

top- [1] N.P. Erugin: Reading Book on the General Course of Differential Equations, Nauka&Technica, Minsk, 1979.
- [2] V.I. Zubov: Lectures on the Control Theory, Nauka, Moscow, 1975.
- [3] V.N. Laptinsky: COnstructive Analysis of Controlled Oscillating Systems, Institute of Mathematics, NAS of Belarus, Minsk, 1998.
- [4] V.B. Larin: Control of Walking Apparatuses, Naukova Dumka, Kiev, 1980.
- [5] V.I. Mironenko: Linear Dependence of Functions along Solutions of Differential Equations, Belarussian State University, Minsk, 1981.
- [6] Yu.I. Paraev: Lyapunov and Riccati Equations, State University, Tomsk, 1989.
- [7] Ia. N. Roytenberg: Automatic Control, Nauka, Moscow, 1978.
- [8] A.M. Samoilenko, V.N. Laptinsky, K.K. Kenjebaev: Constructive Research Approaches of Periodic and Multipoint Boundary Value Problems, Institute of Mathematics, NAS of Ukraine, Kiev, 1999.
- [9] V.N. Laptinsky and V.V. Pugin: Report Theses of Math. Conf. in memory of Prof. S.G. Kondratenia. Brest, (1998), pp. 23.
- [10] V.N. Laptinsky and I.I. Makovetsky: “On Solvability of the Two-Point Boundary-Value Problem for the Nonlinear Lyapunov Equation”, Herald of the Mogilev State University, Vol. 15, (2003), pp. 176–181. Zbl1069.34023
- [11] B.P. Demidovich: Lectures on the Mathematical Theory of Stability, Nauka, Moscow, 1967.
- [12] F.R. Gantmakher: The Matrix Theory, Nauka, Moscow, 1967.
- [13] L.V. Kantorovich and G.P. Akilov: Functional Analysis, Nauka, Moscow, 1977.

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