Relaxation Problems Involving Second-Order Differential Inclusions
We present relaxation problems in control theory for the second-order differential inclusions, with four boundary conditions, u¨(t)∈F(t,u(t),u˙(t)) a.e. on [0,1]; u(0)=0, u(η)=u(θ)=u(1) and, with m≥3 boundary conditions, u¨(t)∈F(t,u(t),u˙(t)) a.e. on [0,1]; u˙(0)=0, u(1)=∑i=1m-2aiu(ξi), where 0...
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| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/792431 |
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| author | Adel Mahmoud Gomaa |
| author_facet | Adel Mahmoud Gomaa |
| author_sort | Adel Mahmoud Gomaa |
| collection | DOAJ |
| description | We present relaxation problems in control theory for the second-order differential inclusions, with four boundary conditions, u¨(t)∈F(t,u(t),u˙(t)) a.e. on [0,1]; u(0)=0, u(η)=u(θ)=u(1) and, with m≥3 boundary conditions, u¨(t)∈F(t,u(t),u˙(t)) a.e. on [0,1]; u˙(0)=0, u(1)=∑i=1m-2aiu(ξi), where 0<η<θ<1, 0<ξ1<ξ2<⋯<ξm-2<1 and F is a multifunction from [0,1]×ℝn×ℝn to the nonempty compact convex subsets of ℝn. We have results that improve earlier theorems. |
| format | Article |
| id | doaj-art-338f5c0976e942e6866af6731977c37c |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-338f5c0976e942e6866af6731977c37c2025-08-20T02:24:17ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/792431792431Relaxation Problems Involving Second-Order Differential InclusionsAdel Mahmoud Gomaa0Taibah University, Faculty of Applied Science, Department of Applied Mathematics, Al-Madinah, Saudi ArabiaWe present relaxation problems in control theory for the second-order differential inclusions, with four boundary conditions, u¨(t)∈F(t,u(t),u˙(t)) a.e. on [0,1]; u(0)=0, u(η)=u(θ)=u(1) and, with m≥3 boundary conditions, u¨(t)∈F(t,u(t),u˙(t)) a.e. on [0,1]; u˙(0)=0, u(1)=∑i=1m-2aiu(ξi), where 0<η<θ<1, 0<ξ1<ξ2<⋯<ξm-2<1 and F is a multifunction from [0,1]×ℝn×ℝn to the nonempty compact convex subsets of ℝn. We have results that improve earlier theorems.http://dx.doi.org/10.1155/2013/792431 |
| spellingShingle | Adel Mahmoud Gomaa Relaxation Problems Involving Second-Order Differential Inclusions Abstract and Applied Analysis |
| title | Relaxation Problems Involving Second-Order Differential Inclusions |
| title_full | Relaxation Problems Involving Second-Order Differential Inclusions |
| title_fullStr | Relaxation Problems Involving Second-Order Differential Inclusions |
| title_full_unstemmed | Relaxation Problems Involving Second-Order Differential Inclusions |
| title_short | Relaxation Problems Involving Second-Order Differential Inclusions |
| title_sort | relaxation problems involving second order differential inclusions |
| url | http://dx.doi.org/10.1155/2013/792431 |
| work_keys_str_mv | AT adelmahmoudgomaa relaxationproblemsinvolvingsecondorderdifferentialinclusions |