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A Topological Transversality Theorem For Multi-Valued Maps In Locally Convex Spaces With Applications To Neutral Equations

Published online by Cambridge University Press:  20 November 2018

Tomasz Kaczynski  and
Jianhong Wu
Tomasz Kaczynski
Affiliation:
Département de Mathématiques et d'informatique, Université de Sherbrooke, Sherbrooke, Québec
Jianhong Wu
Affiliation:
Département de Mathématiques et d'informatique, Université de Sherbrooke, Sherbrooke, Québec
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Abstract

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The concept of essential map and topological transversality due to A. Granas is extended to multi-valued maps in locally convex spaces and it is next applied to prove the solvability of boundary value problems for certain neutral functional differential equations. In order to achieve a required compactness property, the weak topology in a Sobolev space is considered. The topological tool established in the first part of the paper allows to avoid some obstacles which are encountered when trying to use standard degree-theoretical arguments.

Keywords

34H1034K10Topological transversality in locally convex spacemulti-valued mapsneutral equationsboundary value problems.
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 5 , 01 October 1992 , pp. 1003 - 1013
Copyright
Copyright © Canadian Mathematical Society 1992

References

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