Constructive sufficient conditions for univalent resolvability of a two-point boundary value problem for nonlinear Riccati equation are obtained. An illustrative example is given.
@article{bwmeta1.element.doi-10_2478_BF02475661, author = {V. Laptinsky and I. Makovetsky}, title = {On the two-point boundary-value problem for the Riccati matrix differential equation}, journal = {Open Mathematics}, volume = {3}, year = {2005}, pages = {143-154}, zbl = {1069.34023}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475661} }
V. Laptinsky; I. Makovetsky. On the two-point boundary-value problem for the Riccati matrix differential equation. Open Mathematics, Tome 3 (2005) pp. 143-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475661/
[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. | Zbl 1069.34023
[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.