General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded Perturbations
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,ẋ(t)); A(ẍ(t)))+F(t,x(t),ẋ(t),ẍ(t))+G(x(t),ẋ(t),ẍ(t)) a.e. [0,T], A(ẍ(t))∈K(t,ẋ(t)), a.e. t∈[0,T], x(0)=x0,ẋ(0)=u0, ẍ(0)=υ0,...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/695268 |
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| author | M. Bounkhel B. Al-Senan |
| author_facet | M. Bounkhel B. Al-Senan |
| author_sort | M. Bounkhel |
| collection | DOAJ |
| description | 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,ẋ(t)); A(ẍ(t)))+F(t,x(t),ẋ(t),ẍ(t))+G(x(t),ẋ(t),ẍ(t)) a.e. [0,T], A(ẍ(t))∈K(t,ẋ(t)), a.e. t∈[0,T], x(0)=x0,ẋ(0)=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. |
| format | Article |
| id | doaj-art-873deb36b8b7469cb6fe803841793421 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-873deb36b8b7469cb6fe8038417934212025-02-03T06:06:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/695268695268General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded PerturbationsM. Bounkhel0B. Al-Senan1Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaWe 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,ẋ(t)); A(ẍ(t)))+F(t,x(t),ẋ(t),ẍ(t))+G(x(t),ẋ(t),ẍ(t)) a.e. [0,T], A(ẍ(t))∈K(t,ẋ(t)), a.e. t∈[0,T], x(0)=x0,ẋ(0)=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.http://dx.doi.org/10.1155/2012/695268 |
| spellingShingle | M. Bounkhel B. Al-Senan General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded Perturbations Journal of Applied Mathematics |
| title | General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded Perturbations |
| title_full | General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded Perturbations |
| title_fullStr | General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded Perturbations |
| title_full_unstemmed | General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded Perturbations |
| title_short | General Existence Results for Third-Order Nonconvex State-Dependent Sweeping Process with Unbounded Perturbations |
| title_sort | general existence results for third order nonconvex state dependent sweeping process with unbounded perturbations |
| url | http://dx.doi.org/10.1155/2012/695268 |
| work_keys_str_mv | AT mbounkhel generalexistenceresultsforthirdordernonconvexstatedependentsweepingprocesswithunboundedperturbations AT balsenan generalexistenceresultsforthirdordernonconvexstatedependentsweepingprocesswithunboundedperturbations |