Corneliu Ursescu
Abstract:
In this paper we show that second order tangency conditions are
superfluous not to say useless while discussing the existence
condition for certain second order differential inclusions. In
this regard, a counterexample is provided even in the simpler
setting of second order differential equations, where a substitute
condition is propound. In the setting of differential inclusions,
the corresponding substitute condition allows for us to prove
existence of sufficiently many approximate solutions without the
use of any convexity, measurability, or upper semicontinuity
assumption. Accordingly, some proofs in the related literature are
greatly simplified.
Submitted July 30, 2008. Published January 27, 2009.
Math Subject Classifications: 34A60.
Key Words: Second order differential inclusions;
second order tangency inclusions.
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| Corneliu Ursescu "Octav Mayer" Institute of Mathematics Romanian Academy, Iasi Branch, Romania email: corneliuursescu@yahoo.com |
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