Abstract
A variant of the Bourgin-Yang theorem for
Special Issue
Open AccessTopological and variational methods of nonlinear analysis and their applications
View this Special IssueBourgin-Yang-type theorem for a
Received26 Jun 2005
Accepted01 Jul 2005
Published27 Apr 2006
References
S. A. Antonyan, “Retracts in categories of -spaces,” Izvestiya Akademii Nauk Armyanskoĭ SSR. Seriya Matematika, vol. 15, no. 5, pp. 365–378, 1980, English translation in: Soviet Journal of Contemporary Mathematical Analysis \textbf{15} (1980), 30–43.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, John Wiley & Sons, New York, 1984.
View at: Zentralblatt MATH | MathSciNetT. Bartsch, Topological Methods for Variational Problems with Symmetries, vol. 1560 of Lecture Notes in Mathematics, Springer, Berlin, 1993.
View at: Zentralblatt MATH | MathSciNetV. Benci, “On critical point theory for indefinite functionals in the presence of symmetries,” Transactions of the American Mathematical Society, vol. 274, no. 2, pp. 533–572, 1982.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. G. Bourgin, “On some separation and mapping theorems,” Commentarii Mathematici Helvetici, vol. 29, pp. 199–214, 1955.
View at: Google Scholar | Zentralblatt MATH | MathSciNetG. Bredon, Introduction to Compact Transformation Groups, Academic Press, New York, 1972.
View at: MathSciNetZ. Dzedzej, “Equivariant selections and approximations,” in Topological Methods in Nonlinear Analysis, pp. 25–31, Gdansk Scientific Society, Gdansk, 1997.
View at: Google ScholarB. D. Gel'man, “The Borsuk-Ulam theorem in infinite-dimensional Banach spaces,” Sbornik: Mathematics, vol. 193, no. 1, pp. 83–91, 2002.
View at: Google Scholar | Zentralblatt MATH | MathSciNetB. D. Gel'man, “An infinite-dimensional version of the Borsuk-Ulam theorem,” Functional Analysis and Its Applications, vol. 38, no. 4, pp. 1–5, 2004.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. Holm and E. H. Spanier, “Involutions and Fredholm maps,” Topology, vol. 10, no. 3, pp. 203–218, 1971.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Ize and A. Vignoli, Equivariant Degree Theory, vol. 8 of De Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, 2003.
View at: Zentralblatt MATH | MathSciNetW. Krawcewicz and J. Wu, Theory of Degrees with Applications to Bifurcations and Differential Equations, John Wiley & Sons, New York, 1997.
View at: Zentralblatt MATH | MathSciNetA. Kushkuley and Z. I. Balanov, Geometric Methods in Degree Theory for Equivariant Maps, vol. 1632 of Lecture Notes in Mathematics, Springer, Berlin, 1996.
View at: Zentralblatt MATH | MathSciNetJ. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, vol. 74 of Applied Mathematical Sciences, Springer, New York, 1989.
View at: Zentralblatt MATH | MathSciNetE. Michael, “Continuous selections I,” Annals of Mathematics, vol. 63, pp. 361–382, 1956.
View at: Google Scholar | Zentralblatt MATH | MathSciNetW. Rudin, Functional Analysis, McGraw-Hill, New York, 2nd edition, 1991.
View at: Zentralblatt MATH | MathSciNetH. Steinlein, “Borsuk's antipodal theorem and its generalizations and applications: a survey,” in Topological Methods in Nonlinear Analysis, A. Granas, Ed., vol. 95 of Sém Mathematics Sup., pp. 166–235, Presses de l ' Université of Montréal, Montreal, 1985.
View at: Google Scholar | Zentralblatt MATH | MathSciNetI. A. Wolf, Spaces of Constant Curvature, McGraw-Hill, New York, 1967.
View at: Zentralblatt MATH | MathSciNetC.-T. Yang, “On theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujobo and Dyson I,” Annals of Mathematics, vol. 60, pp. 262–282, 1954.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. P. Zhelobenko, Introduction to Representation Theory, Factorial Press, Moscow, 2001.
D. P. Zhelobenko and A. I. Shtern, Representations of Lie Groups, Nauka, Moscow, 1983.
View at: Zentralblatt MATH | MathSciNet
Copyright
Copyright © 2006 Sergey A. Antonyan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.