Title
Analytic Theory Of Global Bifurcation: An Introduction (Princeton Series In Applied Mathematics),Used
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Rabinowitz's classical global bifurcation theory, which concerns the study inthelarge of parameterdependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions of global extent. Even when the operators are infinitely differentiable in all the variables and parameters, connectedness here cannot in general be replaced by pathconnectedness. However, in the context of realanalyticity there is an alternative theory of global bifurcation due to Dancer, which offers a much stronger notion of parameter dependence.This book aims to develop from first principles Dancer's global bifurcation theory for oneparameter families of realanalytic operators in Banach spaces. It shows that there are globally defined continuous and locally realanalytic curves of solutions. In particular, in the realanalytic setting, local analysis can lead to global consequencesfor example, as explained in detail here, those resulting from bifurcation from a simple eigenvalue. Included are accounts of analyticity and implicit function theorems in Banach spaces, classical results from the theory of finitedimensional analytic varieties, and the links between these two and global existence theory.Laying the foundations for more extensive studies of realanalyticity in infinitedimensional problems and illustrating the theory with examples, Analytic Theory of Global Bifurcation is intended for graduate students and researchers in pure and applied analysis.
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