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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 20 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461181491

Mathematical Reviews number (MathSciNet)
MR2839520

Zentralblatt MATH identifier
1232.34025

Citation

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. https://projecteuclid.org/euclid.tmna/1461181491


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