[Propriétés topologiques des ensembles de solutions d'inclusions fonctionnelles partielles d'évolution]
Cette Note traite des inclusions fonctionnelles d'évolution de type neutre dans les espaces de Banach, aussi bien lorsque le semi-groupe est compact que lorsqu'il est non compact. Nous étudions les propriétés topologiques de l'ensemble des solutions. Nous montrons que cet ensemble est non vide, compact, et qu'il est un -ensemble. Ceci signifie qu'il peut ne pas être réduit à un point, mais qu'il est équivalent, pour la topologie algébrique, à un espace réduit à un point. Plus précisément, l'ensemble des solutions a les mêmes groupes d'homologie qu'un ensemble réduit à un point. Comme exemple d'application, nous considérons enfin une inclusion différentielle partielle.
This paper deals with functional evolution inclusions of neutral type in Banach space when the semigroup is compact as well as noncompact. The topological properties of the solution set is investigated. It is shown that the solution set is nonempty, compact and an -set which means that the solution set may not be a singleton but, from the point of view of algebraic topology, it is equivalent to a point, in the sense that it has the same homology group as one-point space. As a sample of application, we consider a partial differential inclusion at end of the paper.
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@article{CRMATH_2017__355_1_45_0,
author = {Zhou, Yong and Peng, Li},
title = {Topological properties of solution sets for partial functional evolution inclusions},
journal = {Comptes Rendus. Math\'ematique},
pages = {45--64},
publisher = {Elsevier},
volume = {355},
number = {1},
year = {2017},
doi = {10.1016/j.crma.2016.11.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.11.011/}
}
TY - JOUR AU - Zhou, Yong AU - Peng, Li TI - Topological properties of solution sets for partial functional evolution inclusions JO - Comptes Rendus. Mathématique PY - 2017 SP - 45 EP - 64 VL - 355 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.11.011/ DO - 10.1016/j.crma.2016.11.011 LA - en ID - CRMATH_2017__355_1_45_0 ER -
%0 Journal Article %A Zhou, Yong %A Peng, Li %T Topological properties of solution sets for partial functional evolution inclusions %J Comptes Rendus. Mathématique %D 2017 %P 45-64 %V 355 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.11.011/ %R 10.1016/j.crma.2016.11.011 %G en %F CRMATH_2017__355_1_45_0
Zhou, Yong; Peng, Li. Topological properties of solution sets for partial functional evolution inclusions. Comptes Rendus. Mathématique, Tome 355 (2017) no. 1, pp. 45-64. doi : 10.1016/j.crma.2016.11.011. http://www.numdam.org/articles/10.1016/j.crma.2016.11.011/
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