Electron. J. Diff. Eqns., Vol. 2009(2009), No. 23, pp. 1-17.

Second order tangency conditions and differential inclusions: a counterexample and a remedy

Corneliu Ursescu

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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