Block diagonalization of systems with measurable coefficients

• Autores: Raúl Naulin
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 13, Nº. 1, 1994, págs. 2-7
• Idioma: inglés
• DOI: 10.22199/S07160917.1994.0001.00002
• Enlaces
  • Texto completo
• Resumen

  • In this paper we show that, previous results given by Coppel concerning the existence of projection matrix P, and a change of variable x = S(t)y reducing system x = A(t)x, where A(t) is a continuous matrix function, to the form y= A(t)y, with the property P A(t) = A(t)P, can be extended to the case when A(t) is a locally integrable function.

• Referencias bibliográficas
  • Citas [1] Agarwal, R.P., Difference Equations and lnequalities, Pure and Aplied Mathematics, Marcel Dekker, New York, 1992.
  • [2] Bainov, D.D., Simeonov, P.S., Systems with Impulse Effect, Ellis Horwood and John Wiley, New York, 1989
  • [3] Coddington E., Levinson N., Theory of Ordinary Differential Equations, McGraw Hill, New York, 1955.
  • [4] Cooke, K., Asymptotic theory for the delay differential equation, ul = -au(t-r(t)), J. Math. An. and App., Vol. 19, 1, pp. 160-173,...
  • [5] Coppel W.A., Dichotomies and reducibility, Journal of differential equations 3. 500-.521, (1967).
  • [6] Coppel W.A., Dichotomies in Stability Theory, Lectures Notes in Mathematics, 629, Springer-Verlag, Berlin, 1978.
  • [7] Kreyszing E., Introductory Functional Analysis with Applications, John Wiley, New York, 1978.
  • [8] Lee E., Markus L., Foundations of Optimal Control Theory, John Wiley and Sons, New York, 1967.
  • [9] Naulin R., Dichotomies for systems with unbounded coefficients, IMA, UCV, Valparaíso, 1992 (Preprint).
  • [10] Naulin, R., Pinto, M., Block diagonalization of linear impulsive systems, Facultad de Ciencias, Universidad de Chile, 1 992(preprint).
  • [11] Palmer, K., Exponential dichotomies and transversal homoclinic points, J. Diff. Eqns., 55, pp. 22.5-256, 1984.
  • [12] Prodi G., Ambrosetti A., Analisi non Lineare, 1 Quaderno, Scuola Normale Superiore, Pisa, 1973.