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, 1-17

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 ( x ̈ ( t ) ) ) + F ( t , x ( t ) , x ̇ ( t ) , x ̈ ( t ) ) + G ( x ( t ) , x ̇ ( t ) , x ̈ ( t ) )          a . e .    [ 0 , T ] , A ( x ̈ ( t ) ) ∈ K ( t , x ̇ ( t ) ) , a.e.       t ∈ [ 0 , T ] , x ( 0 ) = x 0 , x ̇ ( 0 ) = u 0 , x ̈ ( 0 ) = υ 0 , 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:hin:jnljam:695268

DOI: 10.1155/2012/695268

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