A multiplicity result for a system of real integral equations by use of the Nielsen number

Andrei Borisovich; Zygfryd Kucharski; Wacław Marzantowicz

Banach Center Publications (1999)

  • Volume: 49, Issue: 1, page 9-18
  • ISSN: 0137-6934

Abstract

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We prove an existence and multiplicity result for solutions of a nonlinear Urysohn type equation (2.14) by use of the Nielsen and degree theory in an annulus in the function space.

How to cite

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Borisovich, Andrei, Kucharski, Zygfryd, and Marzantowicz, Wacław. "A multiplicity result for a system of real integral equations by use of the Nielsen number." Banach Center Publications 49.1 (1999): 9-18. <http://eudml.org/doc/208971>.

@article{Borisovich1999,
abstract = {We prove an existence and multiplicity result for solutions of a nonlinear Urysohn type equation (2.14) by use of the Nielsen and degree theory in an annulus in the function space.},
author = {Borisovich, Andrei, Kucharski, Zygfryd, Marzantowicz, Wacław},
journal = {Banach Center Publications},
keywords = {index; Nielsen class; Nielsen number; systems of nonlinear integral equations of Urysohn type; Banach space},
language = {eng},
number = {1},
pages = {9-18},
title = {A multiplicity result for a system of real integral equations by use of the Nielsen number},
url = {http://eudml.org/doc/208971},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Borisovich, Andrei
AU - Kucharski, Zygfryd
AU - Marzantowicz, Wacław
TI - A multiplicity result for a system of real integral equations by use of the Nielsen number
JO - Banach Center Publications
PY - 1999
VL - 49
IS - 1
SP - 9
EP - 18
AB - We prove an existence and multiplicity result for solutions of a nonlinear Urysohn type equation (2.14) by use of the Nielsen and degree theory in an annulus in the function space.
LA - eng
KW - index; Nielsen class; Nielsen number; systems of nonlinear integral equations of Urysohn type; Banach space
UR - http://eudml.org/doc/208971
ER -

References

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  1. [BKM1] A. Yu. Borisovich, Z. Kucharski and W. Marzantowicz, Nielsen number and lower estimate for the number of solutions to a certain system of nonlinear integral equations, in: Applied Aspects of Global Analysis. New Developments in Global Analysis series, Voronezh University Press, 1994, 3-11. Zbl0853.45009
  2. [BKM2] A. Yu. Borisovich, Z. Kucharski and W. Marzantowicz, Relative Nielsen number and a lower estimate of the number of components of an algebraic set, in: Global and Stochastic Analysis. New Developments in Global Analysis series, Voronezh University Press, 1995, 3-14. 
  3. [N1] J. Nielsen, Über die Minimalzahl der Fixpunkte bei Abbildungstypen der Ringflächen, Math. Ann. 82 (1921), 83-93. Zbl47.0527.03
  4. [N2] J. Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, I-III, Acta Math. 50, 53, 58 (1927, 1929, 1932), 189-358, 1-76, 87-167. 
  5. [W] F. Wecken, Fixpunktklassen, I-III, Math. Ann. 117, 118, 118 (1941, 1942, 1942), 659-671, 216-234, 544-577. 
  6. [J] B. J. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14 (1983). Zbl0512.55003
  7. [Br1] R. Brown, A topological bound on the number of distinct zeros of an analytic function, Pacific J. Math. 118 (1983), 53-58. 
  8. [Br2] R. Brown, Nielsen fixed point theory and parametrized differential equations, Contemp. Math. 72 (1988), 33-46. 
  9. [Br3] R. Brown, Retraction methods in the Nielsen fixed point theory, Pacific J. Math. 115 (1984), 277-297. Zbl0514.55003
  10. [Br4] R. Brown, The Lefschetz Fixed Point Theorem, Chicago, 1972. 
  11. [Sch] H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986), 253-266. 
  12. [K] Kiang Tsai-han, The Theory of Fixed Point Classes, Springer, Berlin, 1989. Zbl0676.55001
  13. [S] K. Scholz, The Nielsen fixed point theory for non-compact spaces, Rocky Mountain J. Math. 4 (1974), 81-87. Zbl0275.55013
  14. [F] M. Fečkan, Nielsen fixed point theory and nonlinear equations, J. Differential Equations 106 (1993), 312-331. Zbl0839.47041

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