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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1537-744X |