Geodesic
Second order tangency conditions and differential inclusions: a counterexample and a remedy
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34A60
Keywords: second order differential inclusions, second order tangency inclusions 
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     author = {Ursescu, Corneliu},
     title = {Second order tangency conditions and differential inclusions: a counterexample and a remedy},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a188/}
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Ursescu, Corneliu. Second order tangency conditions and differential inclusions: a counterexample and a remedy. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a188/