Second-order viability problem: a baire category approach

• Autorzy: Aitalioubrahim M. , Sajid S.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with the existence of viable solutions to the differential inclusion x(t) ∈ ƒ(t, x(t)) + ext F(t, x(t)), where ƒ 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.

Słowa kluczowe

EN

viability; differential inclusion; extreme points; Baire category theorem

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 1
• Strony: 9--23
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Aitalioubrahim M.

autor

Sajid S.

• U.F.R. Mathematics and Applications, F.S.T., University Hassan II-Mohammedia, BP 146, Mohammedia, Morocco,

Bibliografia

• [1] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer, 1984.
• [2] A. Ben-Tal, Second-order theory of extremum problems, in: Extremal Methods and System Analysis (Austin, TX, 1977), A. V. Fiacco and K. O. Kortanek (eds.), Lecture Notes in Econom. Math. Systems 174, Springer, 1980, 336-356.
• [3] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, 1984.
• [4] B. Cornet et G. Haddad, Théorėme de viabilité pour les inclusions différentielles du second ordre, Israel J. Math. 57 (1987), 225-238.
• [5] F. S. De Blasi and G. Pianigiani, A Baire category approach to the existence of solutions of multivalued differential equations in Banach spaces, Funkcial. Ekvac. 25 (1982), 153-162.
• [6] F. S. De Blasi and G. Pianigiani, The Baire category method in existence problems for a class of multivalued differential equations with nonconvex right hand side, ibid. 28 (1985), 139-156.
• [7] F. S. De Blasi and G. Pianigiani, Differential inclusions in Banach spaces, J. Differential Equations 66 (1987), 208-229.
• [8] M. Marques, Sur la frontiėre d’un convexe mobile, in: Séminaire d’analyse convexe, Montpellier, exp. 12 (1983).
• [9] R. Morchadi and S. Sajid, Non-convex second-order differential inclusion, Bull. Polish Acad. Sci. Math. 47 (1999), 267-281.
• [10] G. Pianigiani, Differential inclusions. The Baire category method, in: Methods of Nonconvex Analysis (Varenna, 1989), A. Cellina (ed.), Lecture Notes in Math. 1446, Springer, 1990, 104-136.
• [11] S. Sajid, Perturbation d’une inclusion différentielle non convexe avec viabilité, C. R. Math. Rep. Acad. Sci. Canada 23 (2001), 33-38.