Periodic solutions of the Riccati equation in Banach spaces

• Autorzy: Baris J. , Buraczewski A.
• Języki publikacji: EN

Abstrakty

EN

In this paper we study the problem of the existence and the construction of periodic solutions of the Riccati equation with continuous periodic coefficients denned on the real line with values in Banach space.

Słowa kluczowe

EN

Riccati equation; periodic solution; spectrum; Green functions; integral equation; Banach space

PL

przestrzeń Banacha; równania Riccatiego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 2
• Strony: 343--353
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Baris J.

• Faculty of Mathematics and Informatics, WM University, ul. Żołnierska 14A, 10-561 Olsztyn, Poland

autor

Buraczewski A.

• The College of Economics and Computer Science, Wyzwolenia 30, 10-106 Olsztyn, Poland

Bibliografia

• [1] V. M. Adamjan, H. Langer and Ch. Tretter, Existence and uniqueness of contractive solutions of some Riccati equations, J. Funct. Anal. 179 (2001), 448-473.
• [2] B. Aulbach, T. Wanner, The Hartman-Grobman theorem for Caratheodory-type differential equations in Banach spaces, Nonlinear Analysis 40 (2000), 91-104.
• [3] Ja. S. Baris, Integral manifolds and solutions of matrix Riccati equation, Dokl. Akad. Nauk. Ukrain. SSR, Ser. A, 11 (1986) 7-10 (in Russian).
• [4] Ja. S. Baris, On the method of constructing approximate integral manifolds, Dokl. Akad. Nauk. 301 (1988), N2; English transl. in Soviet Math. Dokl. 38 (1989), 57-59.
• [5] Ja. S. Baris, O. B. Lykowa, Integral manifolds and the reduction principle in stability theory, Dokl. Akad. Nauk. 311 (1990), N2; English transl. in Soviet Dokl. Math. 41 (1990), 232-235.
• [6] N. N. Bogoliubov, Y. A. Mitropolskii, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York, 1961.
• [7] I. Carr, Applications of Centre Manifold Theory, Springer, New York, 1981.
• [8] J. L. Daleckii, M. G. Krein, Stability of Solutions of Differential Equations in Banach Spaces, AMS Math. Monographs, vol. 43, Amer. Math. Soc., Providence, 1995.
• [9] O. B. Lykova and J. S. Baris, Approximate Integral Manifolds, "Naukova Dumka", Kiev, 1993 (in Russian).
• [10] Ju. A. Mitropolskii, O. B. Lykowa, Integral Manifolds in Nonlinear Mechanics, Nauka, Moscow, 1973 (in Russian).
• [11] K. Schneider, J. S. Baris, O. B. Lykova, S. A. Nakonechna, Qualitative analysis of some dynamical system of hydrodynamical type, Proc. Inter. Conf. Modern Mathem. Problems, part 3, Inst, of Mathematics NAS of Ukraine, Kiev, 1998, 226-230.