This article is cited in 6 papers

Infinite-dimensional version of the Poincare–Hopf theorem and homological characteristics of functionals

V. S. Klimov

P. G. Demidov Yaroslavl State University

Abstract: A version of the Poincare–Hopf theorem is established for multivalued vector fields on submanifolds of a reflexive space. The connection between the critical values and homological characteristics of the Lebesgue sets of Lipschitz functionals is studied. Applications to the theory of operator inclusions with parameters are indicated.

UDC: 517.946

MSC: Primary 58B05, 57R25; Secondary 47J25

Received: 08.12.1999

DOI: 10.4213/sm535

 English version: Sbornik: Mathematics, 2001, 192:1, 49–64

Bibliographic databases:

• 
• 
• 
•