Mihaly Pituk, Department of Mathematics and Computing, University of Veszprem, P. O. Box 158, 8201 Veszprem, Hungary, e-mail: pitukm@almos.vein.hu
Abstract: Consider the delay differential equation
\dot x(t)=g(x(t),x(t-r)),\tag1
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 (MSC 2000): 34K25, 34K12
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