General Existence Results for Third‐Order Nonconvex State‐Dependent Sweeping Process with Unbounded Perturbations

M. Bounkhel and B. Al-Senan

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: We prove the existence of solutions for third‐order nonconvex state‐dependent sweeping process with unbounded perturbations of the form: -A(x(3)(t))∈N(K(t,x.(t)); A(ẍ(t)))+F(t,x(t),x.(t),ẍ(t))+G(x(t),x.(t),ẍ(t)) a.e. [0,T], A(ẍ(t))∈K(t,x.(t)), a.e. t ∈ [0, T], x(00)=x0,x.()=u0, ẍ(0)=υ0, where T > 0, K is a nonconvex Lipschitz set‐valued mapping, F is an unbounded scalarly upper semicontinuous convex set‐valued mapping, and G is an unbounded uniformly continuous nonconvex set‐valued mapping in a separable Hilbert space ℍ.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:695268

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