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CONSTRAINED OPEN MAPPING THEOREMS AND APPLICATIONS

Published online by Cambridge University Press:  01 December 1999

W. BIAN  and
J. R. L. WEBB
W. BIAN
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW; [email protected], [email protected]
J. R. L. WEBB
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW; [email protected], [email protected]
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Abstract

Some constrained open mapping theorems are obtained via Ekeland's variational principle. The constraint need only be a closed subset when the mapping is assumed to be Lipschitz, or a closed convex cone when the mapping is assumed to be closed. Generalizations of some previous results of Welsh and others are obtained. Apart from the presence of a constraint and a different method, the differentiability assumptions made are weaker. As applications, two results on the constrained controllability of nonlinear systems are given.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 3 , December 1999 , pp. 897 - 911
Copyright
The London Mathematical Society 1999

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