Global bifurcation for generalized k-set contractions

Modifying a bifurcation result of Stuart for k-set contractions, we show global bifurcation of the nonlinear equation u=λGu associated with the countably k-set contractive operator G in a real Banach space when λ0 is a characteristic value of the linearization of odd multiplicity. The main tools are Whyburn's lemma and an index formula for countably k-set contractive operators.