The paper deals with the existence of viable solutions to the differential inclusion ẍ(t) ∈ f(t,x(t)) + ext F(t,x(t)), where f is a single-valued map and ext F(t,x) stands for the extreme points of a continuous, convex and noncompact set-valued mapping F with nonempty interior.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-2, author = {Myelkebir Aitalioubrahim and Said Sajid}, title = {Second-Order Viability Problem: A Baire Category Approach}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {57}, year = {2009}, pages = {9-23}, zbl = {1179.34066}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-2} }
Myelkebir Aitalioubrahim; Said Sajid. Second-Order Viability Problem: A Baire Category Approach. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) pp. 9-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-2/