Topological Methods in Nonlinear Analysis

A Borsuk-type theorem for some classes of perturbed Fredholm maps

Pierluigi Benevieri and Alessandro Calamai

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Abstract

We prove an odd mapping theorem of Borsuk type for locally compact perturbations of Fredholm maps of index zero between Banach spaces. We extend this result to a more general class of perturbations of Fredholm maps, defined in terms of measure of noncompactness.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 35, Number 2 (2010), 379-394.

Dates
First available in Project Euclid: 21 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461251013

Mathematical Reviews number (MathSciNet)
MR2676823

Zentralblatt MATH identifier
1215.47050

Citation

Benevieri, Pierluigi; Calamai, Alessandro. A Borsuk-type theorem for some classes of perturbed Fredholm maps. Topol. Methods Nonlinear Anal. 35 (2010), no. 2, 379--394. https://projecteuclid.org/euclid.tmna/1461251013


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References

  • P. Benevieri, A. Calamai and M. Furi, A degree theory for a class of perturbed Fredholm maps , Fixed Point Theory Appl., 2(2005), 185–206 \ref\key 2 ––––, A degree theory for a class of perturbed Fredholm maps \romII, Fixed Point Theory Appl., 2006(2006), 20 pp \ref\key 3
  • P. Benevieri and M. Furi, A simple notion of orientability for Fredholm maps of index zero between Banach manifolds and degree theory , Ann. Sci. Math. Québec, 22(1998), 131–148 \ref\key 4 ––––, On the concept of orientability for Fredholm maps between real Banach manifolds , Topol. Methods Nonlinear Anal., 16(2000), 279–306 \ref\key 5 ––––, Degree for locally compact perturbations of Fredholm maps in Banach spaces , Abstr. Appl. Anal., 2006 , 20 pp \ref\key 6
  • A. Calamai, The invariance of domain theorem for compact perturbations of nonlinear Fredholm maps of index zero , Nonlinear Funct. Anal. Appl., 9(2004), 185–194 \ref\key 7 ––––, A degree theory for a class of noncompact perturbations of Fredholm maps , Ph.D. Thesis, Università di Firenze (2005) \ref\key 8
  • G. Darbo, Punti uniti in trasformazioni a codominio non compatto , Rend. Sem. Mat. Univ. Padova, 24(1955), 84–92 \ref\key 9
  • K. Deimling, Nonlinear Functional Analysis, Springer, Berlin (1985) \ref\key 10
  • J. Dugundji, An extension of Tietze's theorem , Pacific J. Math., 1(1951), 353–367 \ref\key 11
  • D. E. Edmunds and J. R. L. Webb, Remarks on nonlinear spectral theory , Boll. Un. Mat. Ital. B (6), 2(1983), 377–390 \ref\key 12
  • M. Furi, M. Martelli and A. Vignoli, Contributions to spectral theory for nonlinear operators in Banach spaces , Ann. Mat. Pura Appl., 118(1978), 229–294 \ref\key 13
  • T. Kato, Perturbation Theory for Linear Operators , Grundl. Math. Wess., 132 , Springer, Berlin (1980) \ref\key 14
  • C. Kuratowski, Topologie , Monografie Matematyczne, 20 , Warszawa (1958) \ref\key 15
  • N. G. Lloyd, Degree Theory, Cambridge University Press, Cambridge (1978) \ref\key 16
  • L. Nirenberg, Topics in Nonlinear Functional Analysis, Courant Institute of Mathematical Sciences, New York (1974) \ref\key 17
  • R. D. Nussbaum, Degree theory for local condensing maps , J. Math. Anal. Appl., 37(1972), 741–766 \ref\key 18
  • V. G. Zvyagin and N. M. Ratiner, Oriented degree of Fredholm maps of nonnegative index and its application to global bifurcation of solutions , Global Analysis – Studies and Applications V, 111–137, Lecture Notes in Math., 1520 , Springer, Berlin (1992)