Differential inclusions with nonlocal conditions: existence results and topological properties of solution sets
Keywords
Differential inclusions, nonlocal conditions, solution set, compactness, $R_{\delta}$, $R_\delta$-contractibility, acyclicity, proximate retract, tangential conditions, viable solutionsAbstract
In this paper, we study the topological structure of solution sets for the first-order differential inclusions with nonlocal conditions: $$ \cases y'(t) \in F(t,y(t)) &\text{a.e } t\in [0,b],\\ y(0)+g(y)=y_0, \endcases $$ where $F\colon [0,b]\times \mathbb{R}^n\to{\mathcal P}(\mathbb{R}^n)$ is a multivalued map. Also, some geometric properties of solution sets, $R_{\delta}$, $R_\delta$-contractibility and acyclicity, corresponding to Aronszajn-Browder-Gupta type results, are obtained. Finally, we present the existence of viable solutions of differential inclusions with nonlocal conditions and we investigate the topological properties of the set constituted by these solutions.Downloads
Published
2011-04-23
How to Cite
1.
GRAEF, John R., HENDERSON, Johnny and OUAHAB, Abdelghani. Differential inclusions with nonlocal conditions: existence results and topological properties of solution sets. Topological Methods in Nonlinear Analysis. Online. 23 April 2011. Vol. 37, no. 1, pp. 117 - 145. [Accessed 24 April 2024].
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