Asymptotic constancy for nonhomogeneous linear differential equations with unbounded delays

Pages: 100 - 107, Issue Special, July 2003

 Abstract        Full Text (162.5K)              

Hüseyin Bereketoğlu - Department of Mathematics, Faculty of Sciences, Ankara University, 06100 Tandoğan-Ankara, Turkey (email)
Mihály Pituk - Department of Mathematics and Computing, University of Veszprém, P.O. Box 158, 8201 Veszprém, Hungary (email)

Abstract: Sufficient conditions are given for the asymptotic constancy of the solutions of a nonhomogeneous linear delay differential equation with unbounded delays. Moreover, it is shown that the limits of the solutions, as $t \to \infty$, can be computed in terms of the initial function and a special matrix solution of the corresponding adjoint equation.

Keywords:  Delay differential equation, nonhomogeneous linear equation, asymptotic constancy, adjoint equation.
Mathematics Subject Classification:  Primary 34K06, 34K25.

Received: August 2002;      Revised: March 2003;      Published: April 2003.