Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces
In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t)∈F(t,x(t)) a.e. on I, x(t)∈S, ∀t∈I, x(0)=x0∈S, (*), where S is a closed subset in a Banach space 𝕏, I=[0,T], (T>0), F:I×S→𝕏, is an upper semicontinuous set-valued mappin...
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/591620 |
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| author | Messaoud Bounkhel |
| author_facet | Messaoud Bounkhel |
| author_sort | Messaoud Bounkhel |
| collection | DOAJ |
| description | In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t)∈F(t,x(t)) a.e. on I, x(t)∈S, ∀t∈I, x(0)=x0∈S, (*), where S is a closed subset in a Banach space 𝕏, I=[0,T], (T>0), F:I×S→𝕏, is an upper semicontinuous set-valued mapping with convex values satisfying F(t,x)⊂c(t)x+xp𝒦, ∀(t,x)∈I×S, where p∈ℝ, with p≠1, and c∈C([0,T],ℝ+). The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces. |
| format | Article |
| id | doaj-art-0454bdb3bafa48df80bb287526419ec1 |
| institution | OA Journals |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-0454bdb3bafa48df80bb287526419ec12025-08-20T02:03:07ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/591620591620Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach SpacesMessaoud Bounkhel0Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaIn the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t)∈F(t,x(t)) a.e. on I, x(t)∈S, ∀t∈I, x(0)=x0∈S, (*), where S is a closed subset in a Banach space 𝕏, I=[0,T], (T>0), F:I×S→𝕏, is an upper semicontinuous set-valued mapping with convex values satisfying F(t,x)⊂c(t)x+xp𝒦, ∀(t,x)∈I×S, where p∈ℝ, with p≠1, and c∈C([0,T],ℝ+). The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.http://dx.doi.org/10.1155/2013/591620 |
| spellingShingle | Messaoud Bounkhel Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces The Scientific World Journal |
| title | Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces |
| title_full | Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces |
| title_fullStr | Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces |
| title_full_unstemmed | Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces |
| title_short | Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces |
| title_sort | existence results for differential inclusions with nonlinear growth conditions in banach spaces |
| url | http://dx.doi.org/10.1155/2013/591620 |
| work_keys_str_mv | AT messaoudbounkhel existenceresultsfordifferentialinclusionswithnonlineargrowthconditionsinbanachspaces |