### Viability for upper semicontinuous differential inclusions without convexity

#### Abstract

The aim of this paper is to prove the existence result of viable solutions

for the differential inclusion

$$

\dot{x}(t) \in F(x(t)),\qquad x(t) \in K\quad \text{on } [0,T],

$$

where $F$ is an upper semicontinuous set-valued map with compact values.

for the differential inclusion

$$

\dot{x}(t) \in F(x(t)),\qquad x(t) \in K\quad \text{on } [0,T],

$$

where $F$ is an upper semicontinuous set-valued map with compact values.

#### Keywords

Regularity; upper semicontinuous; Clarke subdifferential

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