Multiple perturbed solutions near nondegenerate manifolds of solutions

Michal Fečkan

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 4, page 635-643
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Fečkan, Michal. "Multiple perturbed solutions near nondegenerate manifolds of solutions." Commentationes Mathematicae Universitatis Carolinae 34.4 (1993): 635-643. <http://eudml.org/doc/247525>.

@article{Fečkan1993,
abstract = {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.},
author = {Fečkan, Michal},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Nielsen fixed point theory; perturbations; nondegenerate manifolds; perturbed equation; multiple solutions; Nielsen fixed point theory},
language = {eng},
number = {4},
pages = {635-643},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Multiple perturbed solutions near nondegenerate manifolds of solutions},
url = {http://eudml.org/doc/247525},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Fečkan, Michal
TI - Multiple perturbed solutions near nondegenerate manifolds of solutions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 4
SP - 635
EP - 643
AB - 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.
LA - eng
KW - Nielsen fixed point theory; perturbations; nondegenerate manifolds; perturbed equation; multiple solutions; Nielsen fixed point theory
UR - http://eudml.org/doc/247525
ER -

References

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  1. Fečkan M., Nielsen fixed point theory and nonlinear equations, to appear in Journal Differential Equations. 
  2. Mawhin J., Willem M., Critical Point Theory and Hamiltonian Systems, in Appl. Math. Sci., Vol. 74 (1989). (1989) Zbl0676.58017MR0982267
  3. Brown R.F., Topological identification of multiple solutions to parametrized nonlinear equations, Pacific J. Math. 131 (1988), 51-69. (1988) Zbl0615.47042MR0917865
  4. Golubitsky M., Guillemin V., Stable Mappings and their Singularities, Springer-Verlag New York (1973). (1973) Zbl0294.58004MR0341518
  5. Jiang B., Lectures on Nielsen Fixed Point Theory, in Contemporary Math., Vol 14 (1983). (1983) Zbl0512.55003MR0685755
  6. Dancer E.N., The G-invariant implicit function theorem in infinite dimensions II, Proc. Royal Soc. Edinburgh 102 A, (1986), 211-220. (1986) Zbl0601.58013MR0852355
  7. Ambrosetti A., Bessi U., Multiple closed orbits for perturbed Keplerian problems, Journal Differential Equations 96 (1992), 283-94. (1992) Zbl0759.34033MR1156662
  8. Guckenheimer J., Holmes P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag New York (1983). (1983) Zbl0515.34001MR0709768
  9. Fečkan M., Problems with nonlinear boundary value conditions, Comment. Math. Univ. Carolinae 33 (1992), 597-604. (1992) MR1240180
  10. Hirsch M.W., Differential Topology, Springer-Verlag New York (1976). (1976) Zbl0356.57001MR0448362

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