Annali di Matematica Pura ed Applicata

, Volume 86, Issue 1, pp 115–123 | Cite as

Asymptotic behavior of a perturbed linear differential equation with time lag on a product space

  • Nelson Onuchic


The objective of this paper is to study the asymptotic behavior of the solutions of the differential equation with finite time lag
$$\begin{gathered} \dot x\left( t \right) = L\left( {t,x_t } \right) + X\left( {t,x_t ,y_t } \right) \hfill \\ \dot y\left( t \right) = J\left( {t,y_t } \right) + Y\left( {t,x,y_t } \right) \hfill \\ \end{gathered} $$
by knowing that the zero solution of u(t)=L(t, ut) is uniformly stable, the zero solution of v(t)=J(t, vt) is esponentially stable and X, Y satisfy certain given conditions.


Differential Equation Asymptotic Behavior Finite Time Product Space Linear Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1]
    A. Halanay, —Differential equations, stability, oscillations time lag, Academic Press New York, 1966.Google Scholar
  2. [2]-a-
    J. K. Hale,Asymptotic behavior of the solutions of differential-difference equations, Proc Symp. Nonlinear Oscillations, Kiev, USSR, 1961, II, 409–426.Google Scholar
  3. [2]-b-
    —— ——A class of functional-differential equations, Contributions to differential equations, Vol. I, 4, 1963, 411–423.MathSciNetGoogle Scholar
  4. [3]
    N. Krasovskii,Stability of motion, Stanford Univ. Press, Stanford, California, 1963,Google Scholar
  5. [4]
    N. Onuchic,On the uniform stability of a perturbed linear functional differential equation, Proc. A.M.S., 1968.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1970

Authors and Affiliations

  • Nelson Onuchic
    • 1
  1. 1.São CarlosBrasil

Personalised recommendations