Bifurcation Results for a Class of Perturbed Fredholm Maps
© P. Benevieri and A. Calamai. 2008
Received: 3 March 2008
Accepted: 27 July 2008
Published: 31 July 2008
We prove a global bifurcation result for an equation of the type , where is a linear Fredholm operator of index zero between Banach spaces, and, given an open subset of , are and continuous, respectively. Under suitable conditions, we prove the existence of an unbounded connected set of nontrivial solutions of the above equation, that is, solutions with , whose closure contains a trivial solution . The proof is based on a degree theory for a special class of noncompact perturbations of Fredholm maps of index zero, called -Fredholm maps, which has been recently developed by the authors in collaboration with M. Furi.
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