MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 293-299 (2002)

Convergence to equilibria in a differential equation with small delay

Mihaly Pituk

Mihaly Pituk, Department of Mathematics and Computing, University of Veszprém, P. O. Box 158, 8201 Veszprém, Hungary, e-mail: pitukm@almos.vein.hu

Abstract: Consider the delay differential equation $$ \dot x(t)=g(x(t),x(t-r)),\tag 1 $$ where $r>0$ is a constant and $g \br ^2\rightarrow \br $ is Lipschitzian. It is shown that if $r$ is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.

Keywords: delay differential equation, equilibrium, convergence

Classification (MSC2000): 34K25, 34K12

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