Electron. J. Diff. Eqns., Vol. 2004(2004), No. 50, pp. 1-14.

### Local invariance via comparison functions Ovidiu Carja, Mihai Necula, & Ioan I. Vrabie

Abstract:
We consider the ordinary differential equation , where is a given function, while is an open subset in . We prove that, if is locally closed and there exists a comparison function such that

for each , then is locally invariant with respect to . We show further that, under some natural extra condition, the converse statement is also true.

Submitted June 18, 2003. Published April 6, 2004.
Math Subject Classifications: 34A12, 34A34, 34C05,34C40, 34C99.
Key Words: Viable domain, local invariant subset, exterior tangency condition, comparison property, Lipschitz retract.

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 Ovidiu Carja Faculty of Mathematics, Al. I. Cuza" University 700506 Iasi, Romania email: ocarja@uaic.ro Mihai Necula Faculty of Mathematics, Al. I. Cuza" University 700506 Iasi, Romania email: necula@uaic.ro Ioan I. Vrabie Faculty of Mathematics, Al. I. Cuza" University 700506 Iasi, Romania email: ivrabie@uaic.ro