Note on the existence of a (…)-bounded solution for a Lyapunov matrix differential equation

• Autorzy: Diamandescu A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we give a necessary and sufficient condition for the existence of at least one (…)-bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation. In addition, we give a result in connection with the asymptotic behavior of the (…)-bounded solutions of this equation.

Słowa kluczowe

EN

Lyapunov matrix differential equation

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2012
• Tom: Vol. 45, nr 3
• Strony: 549--560
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Diamandescu A.

• University Of Craiova Department Of Applied Mathematics 13, "Al. I. Cuza" St., 200585 Craiova, Romania,

Bibliografia

• [1] O. Akinyele, On partial stability and boundedness of degree k, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 65(8) (1978), 259–264.
• [2] R. Bellman, Introduction to Matrix Analysis, McGraw-Hill Book Company, Inc. New York, 1960 (translated in Romanian).
• [3] A. Constantin, Asymptotic properties of solutions of differential equations, An. Univ. Timisoara, Ser. Stiinµ. Mat. 30(2–3) 1992, 183–225.
• [4] A. Diamandescu, Note on the -boundedness for the solutions of a system of differential equations, Acta Math. Univ. Comenian. 73(2) (2004), 223–233.
• [5] A. Diamandescu, Existence of -bounded solutions for a system of differential equations, Electron. J. Differential Equations 63 (2004), 1–6.
• [6] A. Diamandescu, -bounded solutions for a Lyapunov matrix differential equation, Electron. J. Qual. Theory Differ. Equ. 17 (2009), 1–11.
• [7] T. G. Hallam, On asymptotic equivalence of the bounded solutions of two systems of differential equations, Michigan Math. J. 16 (1969), 353–363.
• [8] J. Morchalo, On (−L p)-stability of nonlinear systems of differential equations, An. Stiinµ. Univ. Al. I. Cuza Iasi Mat. 4 (1990), 353–360.
• [9] M. S. N. Murty, G. Suresh Kumar, On -boundedness and -stability of matrix Lyapunov systems, J. Appl. Math. Comput. 26 (2008), 67–84.