Existencia y comportamiento asintotico de una clase de ecuaciones con retardo


  • Julio Gallardo P. Universidad de La Frontera.
  • Manuel Pinto Universidad de Chile.




By means of Tychonoff 's Theorem on the fixed point, we obtain existence theorems and asymptotic formulae for the solutions of a certain class of delay-differential equations.

Author Biographies

Julio Gallardo P., Universidad de La Frontera.

Departamento de Matemática.

Manuel Pinto, Universidad de Chile.

Departamento de Matemática.


[1] Cooke, K.: Functional ditferential equations close to differential equations, Bull. Amer. Math. Soc.72, :285-288, 1966.

[2] Cooke, K.: Functional differential equations with asymptotically vanishing lag, Rend. Circ. Mat. Palermo XVI, 39-56, 1967.

[3] Cooke, K .: Asymptotic theory for the delay-differential equations u' (t) = -au(t- r(u(t))), J. Math. Anal. Appl. 19, 160-173, 1967.

[4] Donoso, A.; Pinto, M.: Asymptotic behavior of solution of x'( t) =A(t )x(t-r(t) ), Pre-print University of Chile, 1992.

[5] Gallardo. J.: Pinto, M.: Asymtotic integration of delay-differential systems with time and state dependent, Submitted.

[6] Hale, J.: Functional differential equations, Springer- Verlag, 1977.

[7] Pinto, M.: Asymptotic integration of the functional differential equations, y'(t) = a(t)y(t- r·(t, y)), J. Math. Anal. Appl., 1993, To appear.

[8] Pinto, M.: Green-Liouville formulac for second order delay differential equations, Submitted,

[9] Pinto, M.: Uniform asymptotic stability of solutions of y'(t) = f(t, y(t-r(t))), Submitted,

[10] Pinto, M.: Functional differential equations close to ordinary differential equations, Submitted,

[11] Pinto, M.: Asymptotic behavior of solutions of the functional differential equations x'(t) = a(t)x(r(t)) + bx(t), b ? R, Proyecciones, Vol 10, .59-76, 1991.



How to Cite

J. Gallardo P. and M. Pinto, “Existencia y comportamiento asintotico de una clase de ecuaciones con retardo”, Proyecciones (Antofagasta, On line), vol. 12, no. 1, pp. 45-62, Apr. 2018.