Stability of Critical Values and Isolated Critical Continua |
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Authors: | Michael Reeken |
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Affiliation: | 1. Battelle Institute, Advanced Studies Center, 7, route de Drize, 1227, Carouge-Geneva
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Abstract: | We extend the study of critical points in [4]. We show that isolated components of critical points lying on a levelset can be described by an integer which is a lower bound to the “number” of critical points of any function near to the original one in C1-sup-norm. We also derive a global theorem about continua of critical values similar to that given by Rabinowitz for continua of solutions of certain nonlinear eigenvalue problems. We give a simple application of our abstract results to the problem of bifurcation for gradient systems when the linearization is not completely continuous. |
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