Topological Methods in Nonlinear Analysis

Differential inclusions with nonlocal conditions: existence results and topological properties of solution sets

John R. Graef, Johnny Henderson, and Abdelghani Ouahab

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In this paper, we study the topological structure of solution sets for the first-order differential inclusions with nonlocal conditions: $$ \begin{cases} y'(t) \in F(t,y(t)) &\text{a.e. } t\in [0,b],\\ y(0)+g(y)=y_0, \end{cases} $$ 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.

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Topol. Methods Nonlinear Anal., Volume 37, Number 1 (2011), 117-145.

First available in Project Euclid: 20 April 2016

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Graef, John R.; Henderson, Johnny; Ouahab, Abdelghani. Differential inclusions with nonlocal conditions: existence results and topological properties of solution sets. Topol. Methods Nonlinear Anal. 37 (2011), no. 1, 117--145.

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