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An example of application of the Nielsen theory to integro-differential equations
Authors:
Jan Andres and Tomás Fürst
Journal:
Proc. Amer. Math. Soc. 134 (2006), 1985-1993
MSC (2000):
Primary 34C25, 47H10, 54H25
Posted:
December 19, 2005
MathSciNet review:
2215767
Full-text PDF Free Access
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Abstract: A new nontrivial example of an application of the Nielsen fixed-point theory is presented, this time, to integro-differential equations. The emphasis is on the parameter space so that no subdomain becomes invariant under the related solution (Hammerstein) operator. Thus, at least three (harmonic) periodic solutions are established to a planar integro-differential system.
References
- 1.
J. Andres, A nontrivial example of application of the Nielses fixed-point theory to differential systems: problem of Jean Leray. Proceed. Amer. Math. Soc. 128 (2000), 2921-2931. MR 1664285 (2000m:47074)
- 2.
J. Andres, Nielsen number and differential equations. Fixed Point Th. Appl. 2 (2005), 137-167.
- 3.
J. Andres and L. Górniewicz, Topological Fixed Point Principles for Boundary Value Problems. Kluwer, Dordrecht, 2003. MR 1998968 (2005a:47102)
- 4.
J.-P. Aubin and A. Cellina, Differential Inclusions. Springer, Berlin, 1984. MR 0755330 (85j:49010)
- 5.
K. Borsuk, Theory of Retracts. Polish Sci. Publishers, Warsaw, 1967. MR 0216473 (35:7306)
- 6.
R. F. Brown, On the Nielsen fixed point theorem for compact maps. Duke Math. J. 36 (1969), 699-708. MR 0250290 (40:3529)
- 7.
R. F. Brown, More about Nielsen theories and their applications. In: ``Handbook of Topological Fixed Point Theory'' (R. F. Brown, M. Furi, L. Górniewicz and B. Jiang, eds.), Springer, Berlin, 2005, pp. 433-462. MR 2171114
- 8.
A. Yu. Borisovich, Z. Kucharski and W. Marzantowicz, Nielsen number and lower estimates for the number of solutions to a certain system of nonlinear integral equations. In: ``New Developement in Global Analysis Series'', Voronezh Univ. Press, Voronezh, 1994, pp. 3-10 (in Russian). MR 1321822 (96a:47103)
- 9.
A. Yu. Borisovich, Z. Kucharski and W. Marzantowicz, A multiplicity result for a system of real integral equations by use of the Nielsen number. In: ``Nielsen Theory and Reidemeister Torsion'' (J. Jezierski, ed.), Banach Center Publ. vol. 49, Warsaw, pp. 9-18. MR 1734721 (2000i:55004)
- 10.
M. J. Capinski and K. Wójcik, Isolating segment for Carathéodory systems and existence for periodic solutions. Proceed. Amer. Math. Soc. 131, 8 (2003), 2443-2451. MR 1974642 (2003m:37019)
- 11.
M. Feckan, Nielsen fixed point theory and nonlinear equations. J. Diff. Eqns 106, 2 (1993), 312-331. MR 1251856 (94k:47093)
- 12.
M. Feckan, Multiple solutions of nonlinear equations via Nielsen fixed-point theory: a survey. In: ``Nonlinear Analysis in Geometry and Topology'' (T. M. Rassias, ed.), Hadronic Press, Palm Harbor, FL, 2000, pp. 77-97. MR 1766782 (2001e:47095)
- 13.
A. Granas and J. Dugundji, Fixed Point Theory, Springer, Berlin, 2003. MR 1987179 (2004d:58012)
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Additional Information
Jan Andres
Affiliation:
Department of Mathematical Analysis, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc-Hejcín, Czech Republic
Email:
andres@inf.upol.cz
Tomás Fürst
Affiliation:
Department of Mathematical Analysis, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc-Hejcín, Czech Republic
Email:
tomas.furst@seznam.cz
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08213-4
PII:
S 0002-9939(05)08213-4
Keywords:
Nielsen number,
lower estimate of fixed points,
multiplicity results,
integro-differential equations,
nontrivial application.
Received by editor(s):
January 18, 2005
Received by editor(s) in revised form:
February 8, 2005
Posted:
December 19, 2005
Additional Notes:
This work was supported by the Council of Czech Government (MSM 6198959214).
Communicated by:
Carmen C. Chicone
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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