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Twice degenerate equations in spaces of vector-valued functions. (English) Zbl 0952.47046
The purpose of this paper is to calculate an index at infinity for the following classes of asymptotically linear and asymptotically homogeneous vector fields: $Tx= x- A(x+ f(t,x)+ b(t)),$ respectively $Tx= x- A(x+ f(t,x)+ q(t, x)).$ Applications to a periodic problems for a system of two nonlinear first-order ODE and to a two-point BVP for a system of two nonlinear second-order ODE are also given.
MSC:
 47H11 Degree theory for nonlinear operators 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)