Global bifurcation for generalized image-set contractions Original Research Article

Modifying a bifurcation result of Stuart for kk-set contractions, we show global bifurcation of the nonlinear equation u=λGuu=λGu associated with the countably kk-set contractive operator GG in a real Banach space when λ0λ0 is a characteristic value of the linearization of odd multiplicity. The main tools are Whyburn’s lemma and an index formula for countably kk-set contractive operators.