Existence of viable solutions for nonconvex differential inclusions
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We show the existence result of viable solutions to the differential inclusion
ẋ(t) ∈ G(x(t)) + F(t, x(t))
x(t) ∈ S on [0, T],
where F : [0, T] x H → H (T > 0) is a continuous set-valued mapping, G : H → H is a Hausdorff upper semi-continuous set-valued mapping such that G(x) ⊂ ∂g(x), where g : H → ℝ is a regular and locally Lipschitz function and S is a ball, compact subset in a separate Hilbert space H.
CitationBounkhel, M., & Haddad, T. (2005). Existence of viable solutions for nonconvex differential inclusions. Electronic Journal of Differential Equations, 2005(50), pp. 1-10.
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