Topological Methods in Nonlinear Analysis

On the structure of the solution set of abstract inclusions with infinite delay in a Banach space

Lahcene Guedda

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Abstract

In this paper we study the topological structure of the solution set of abstract inclusions, not necessarily linear, with infinite delay on a Banach space defined axiomatically. By using the techniques of the theory of condensing maps and multivalued analysis tools, we prove that the solution set is a compact $R_\delta$-set. Our approach makes possible to give a unified scheme in the investigation of the structure of the solution set of certain classes of differential inclusions with infinite delay.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 48, Number 2 (2016), 567-595.

Dates
First available in Project Euclid: 21 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1482289230

Digital Object Identifier
doi:10.12775/TMNA.2016.060

Mathematical Reviews number (MathSciNet)
MR3642774

Zentralblatt MATH identifier
1365.34133

Citation

Guedda, Lahcene. On the structure of the solution set of abstract inclusions with infinite delay in a Banach space. Topol. Methods Nonlinear Anal. 48 (2016), no. 2, 567--595. doi:10.12775/TMNA.2016.060. https://projecteuclid.org/euclid.tmna/1482289230


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