# American Institute of Mathematical Sciences

April  1995, 1(2): 207-216. doi: 10.3934/dcds.1995.1.207

## The index at infinity of some twice degenerate compact vector fields

 1 Institute for Information Transmission Problems, Russian Academy, 19 Ermolovoy st., 101447 Moscow, Russian Federation 2 Institut Mathématique Pure et Appliquée, Université Catholique de Louvain, B-1348 Louvain-la-Neuve

Received  November 1994 Published  February 1995

The index at infinity of some compact vector fields associated with Nemytski operators is computed in situations where the linear part is degenerate and the nonlinear part does not satisfy the Landesman-Lazer conditions. Applications are given to the existence and multiplicity of solutions of nonlinear equations depending upon a parameter.
Citation: A.M. Krasnosel'skii, Jean Mawhin. The index at infinity of some twice degenerate compact vector fields. Discrete & Continuous Dynamical Systems, 1995, 1 (2) : 207-216. doi: 10.3934/dcds.1995.1.207
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