Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 23, pp. 1-17.

Title: Second order tangency conditions and differential
       inclusions: a counterexample and a remedy
   
Author: Corneliu Ursescu (Romanian Academy, Iasi Branch, Romania)

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.