WIAS Preprint No. 326, (1997)

Twice degenerate equations in the space of vector-valued functions



Authors

  • Kloeden, Peter E.
  • Krasnosel´skii, Alexander M.

2010 Mathematics Subject Classification

  • 47H11 47H30

Keywords

  • index at infinity, asymptotically linear and asymptotically homogeneous vector fields, periodic problems, system of two nonlinear first-order ODE, nonlinear second-order ODE

Abstract

New results are suggested which allow to calculate an index at infinity for asymptotically linear and asymptotically homogeneous vector fields in spaces of vector-valued functions. The case is considered where both linear approximation at infinity and "linear + homogeneous" approximation are degenerate. Applications are given to the 2π-periodic problem for a system of two nonlinear first order ODE's and to the two-point BVP for a system of two nonlinear second order ODE's.

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