On the solvability of complementarity problems by Leray-Schauder type alternatives (Q2711254)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the solvability of complementarity problems by Leray-Schauder type alternatives |
scientific article |
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6 November 2001
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Hilbert space
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\(\alpha\)-condensing fields
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nonlinear complementarity problems
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Leray-Schauder type alternatives
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existence theorems
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On the solvability of complementarity problems by Leray-Schauder type alternatives (English)
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The author considers nonlinear complementarity problems of the form:NEWLINENEWLINENEWLINEfind \(x_*\in K\) such that \(f(x_*)\in K^*\) and \(\langle x_*,f(x_*) \rangle=0\)NEWLINENEWLINENEWLINEwhere \(K\subset H\) (Hilbert space) is a closed pointed convex cone and \(f\in H\to H\) an arbitrary mapping. For this problem, the author presents two new applications of Leray-Schauder type alternatives: new existence theorems and a generalization to \(\alpha\)-condensing fields.
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