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Journal of the London Mathematical Society 1999 60(3):897-911; doi:10.1112/S0024610799008078
© 1999 by London Mathematical Society
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© The London Mathematical Society

Constrained Open Mapping Theorems And Applications

W. Bian and J. R. L. Webb

Department of Mathematics, University of Glasgow Glasgow G12 8QW, wb{at}maths.gla.ac.uk
Department of Mathematics, University of Glasgow Glasgow G12 8QW, jrlw{at}maths.gla.ac.uk

Received 13 March 1998. Revision received 18 August 1998.

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.


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