A relative variant of the Morse theory

V. S. Klimov

Chair of Mathematical Analysis, Yaroslavl State University, Yaroslavl, Russia

Abstract: We develop a relative variant of the Morse theory for Lipschitz functionals defined on closed subsets of a Banach manifold. We prove the invariance of topological characteristics of functionals under uniform deformations.

Keywords: nonsmooth analysis, functional, space, manifold, critical value.

UDC: 517.946

Received: 13.12.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:1, 17–25

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