General Existence Results for Nonconvex Third Order Differential Inclusions
نویسندگان
چکیده
In this paper we prove the existence of solutions to the following third order differential inclusion: x(3)(t) ∈ F (t, x(t), ẋ(t), ẍ(t)) + G(x(t), ẋ(t), ẍ(t)), a.e. on [0, T ] x(0) = x0, ẋ(0) = u0, ẍ(0) = v0, and ẍ(t) ∈ S,∀t ∈ [0, T ], where F : [0, T ]×H×H×H → H is a continuous set-valued mapping, G : H× H × H → H is an upper semi-continuous set-valued mapping with G(x, y, z) ⊂ ∂g(z) where g : H → R is a uniformly regular function over S and locally Lipschitz and S is a ball compact subset of a separable Hilbert space H.
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