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On a global implicit function theorem for locally Lipschitz maps via non-smooth critical point theory |
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| Authors: | Marek Galewski Marius R?dulescu |
| Institution: | 1. Institute of Mathematics, Lodz University of Technology, Wolczanska 215, 90-924 Lodz, Polandmarek.galewski@p.lodz.pl;3. Academia Romana, Institute of Mathematical Statistics, and Applied Mathematics, Calea 13 Septembrie nr 13, Bucharest, RO-050711, Romania |
| Abstract: | We prove a non-smooth generalization of the global implicit function theorem. More precisely we use the non-smooth local implicit function theorem and the non-smooth critical point theory in order to prove a non-smooth global implicit function theorem for locally Lipschitz functions. A comparison between several global inversion theorems is discussed. Applications to algebraic equations are given. |
| Keywords: | 26B10 58C15 49J52 |