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Bifurcation Results for a Class of Perturbed Fredholm Maps
Fixed Point Theory and Applications volume 2008, Article number: 752657 (2008)
Abstract
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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Benevieri, P., Calamai, A. Bifurcation Results for a Class of Perturbed Fredholm Maps. Fixed Point Theory Appl 2008, 752657 (2008). https://doi.org/10.1155/2008/752657
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DOI: https://doi.org/10.1155/2008/752657