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