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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Second-order viability problem: a baire category approach

Aitalioubrahim M., Sajid S.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

Vol. 57, no 1

9-23

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.

Nonconvex second-order differential inclusion

Morchadi R., Sajid S.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 3

267-281

This paper deals with the local existence of solutions of the differential inclusion x''(t) [belongs to] ext F(t, x(t)), x(0) = x[sub o], x'(0) = v[sub o] [belongs to] T[sub K](x[sub o]) and x(t) [belons to] K where F is a convex and continuous set-valued map with nonempty interior in a Hilbert space, K is a closed convex subset and ext F(t, x(t)) denotes the set of extreme points of F(t, x(t)). Our approach is based on the Baire category theorem.