Existence of Viable Solutions for Nonconvex-Valued Differential Inclusions in Banach Spaces

Truong Xuan Duc Ha

Abstract: A local existence result is proved for the viability problem $$ \dot x(t)\in F(t,x(t)), x(0)=x_{0}, x(t)\in K, $$ where $F(\cdot,\cdot)$ is an integrably bounded, (strongly) measurable in $t$, Lipschitz continuous in $x$ multifunction with closed values and $K$ is a closed subset of a separable Banach space.

Keywords: Viable solution; nonconvex-valued differential inclusion; Banach space.

Classification (MSC2000): 34A60

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