- 10/05/2023 - 15h - CLAV Anfiteatro 1

**Clara Carlota**, Universidade de Évora

Given any

*AC*solution $\overline{x}:[a,b]\rightarrow \mathbb{R}^{n}$ to the convex differential inclusion*x*' (

*t*) in co {

*v*^1(

*t*), ... ,

*v*^

*m*(

*t*) } a.e. on [

*a*,

*b*] ,

we present necessary and sufficient conditions for existence of solution to the associated nonconvex inclusion

*x*'(

*t*) in

*v*^1(

*t*), ... ,

*v*^

*m*(

*t*) } a.e.

*x*(

*a*) =\overline{

*x*}(

*a*)

*x*(

*b*) = \overline{

*x*}(

*b*),

under the extra pointwise constraint

\langle

*x*(

*t*) , \omega \rangle \leq \langle \overline{

*x*}(

*t*) ,\omega \rangle for all

*t*in [

*a*,

*b*]

where \omega is any vector in

*R*^*n*.