Abstract
We show some abstract (purely set-topological) principles which allow to prove the existence of global solution branches. The results apply either for the locally compact situation and then allow to prove global bifurcation results of Rabinowitz type, or they apply for a locally connected situation and allow to prove global branches of arbitrarily small perturbations without any compactness hypotheses. As two applications, we obtain a generalization of the Rabinowitz theorem for bifurcation from an interval and an implicit function type theorem for nondifferentiable functions.
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Väth, M. Global solution branches and a topological implicit function theorem. Annali di Matematica 186, 199–227 (2007). https://doi.org/10.1007/s10231-005-0001-y
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DOI: https://doi.org/10.1007/s10231-005-0001-y