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Bifurcation for families of nonlinear perturbations of closed Fredholm operators of index zero. (English) Zbl 1026.47008

A bifurcation (at infinity) theorem for some families of \(k\)-set contraction perturbations to closed Fredholm operators of index zero is proved in this paper by using a homotopy invariant (parity) and a degree theory adapted to the situation. An application is given to a class of nonlinear Sturm-Liouville problems on the half-line.

MSC:

47A53 (Semi-) Fredholm operators; index theories
58E07 Variational problems in abstract bifurcation theory in infinite-dimensional spaces
34B40 Boundary value problems on infinite intervals for ordinary differential equations
47H11 Degree theory for nonlinear operators
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