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Title: Multiple perturbed solutions near nondegenerate manifolds of solutions (English)
Author: Fečkan, Michal
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 34
Issue: 4
Year: 1993
Pages: 635-643
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Category: math
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Summary: The existence of multiple solutions for perturbed equations is shown near a manifold of solutions of an unperturbed equation via the Nielsen fixed point theory. (English)
Keyword: Nielsen fixed point theory
Keyword: perturbations
Keyword: nondegenerate manifolds
MSC: 34B15
MSC: 34C25
MSC: 58C30
MSC: 58D25
MSC: 58E07
idZBL: Zbl 0795.58006
idMR: MR1263793
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Date available: 2009-01-08T18:06:56Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/118621
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Reference: [1] Fečkan M.: Nielsen fixed point theory and nonlinear equations.to appear in Journal Differential Equations.
Reference: [2] Mawhin J., Willem M.: Critical Point Theory and Hamiltonian Systems.in Appl. Math. Sci., Vol. 74 (1989). Zbl 0676.58017, MR 0982267
Reference: [3] Brown R.F.: Topological identification of multiple solutions to parametrized nonlinear equations.Pacific J. Math. 131 (1988), 51-69. Zbl 0615.47042, MR 0917865
Reference: [4] Golubitsky M., Guillemin V.: Stable Mappings and their Singularities.Springer-Verlag New York (1973). Zbl 0294.58004, MR 0341518
Reference: [5] Jiang B.: Lectures on Nielsen Fixed Point Theory.in Contemporary Math., Vol 14 (1983). Zbl 0512.55003, MR 0685755
Reference: [6] Dancer E.N.: The G-invariant implicit function theorem in infinite dimensions II.Proc. Royal Soc. Edinburgh 102 A, (1986), 211-220. Zbl 0601.58013, MR 0852355
Reference: [7] Ambrosetti A., Bessi U.: Multiple closed orbits for perturbed Keplerian problems.Journal Differential Equations 96 (1992), 283-94. Zbl 0759.34033, MR 1156662
Reference: [8] Guckenheimer J., Holmes P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields.Springer-Verlag New York (1983). Zbl 0515.34001, MR 0709768
Reference: [9] Fečkan M.: Problems with nonlinear boundary value conditions.Comment. Math. Univ. Carolinae 33 (1992), 597-604. MR 1240180
Reference: [10] Hirsch M.W.: Differential Topology.Springer-Verlag New York (1976). Zbl 0356.57001, MR 0448362
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