PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2000 | 75 | 2 | 143-166
Tytuł artykułu

The coincidence index for fundamentally contractible multivalued maps with nonconvex values

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given.
Rocznik
Tom
75
Numer
2
Strony
143-166
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-12-22
poprawiono
2000-05-31
Twórcy
autor
  • Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
  • [1] R. R. Akhmerov, M. I. Kamenskiĭ, A. S. Potapov, A. E. Rodkina and B. N. Sadovskiĭ, Measures of Noncompactness and Condensing Operators, Birkhäuser, Basel, 1992.
  • [2] S. Armentrout and T. M. Price, Decomposition into compact sets with UV properties, Trans. Amer. Math. Soc. 141 (1969), 433-442.
  • [3] Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis and V. V. Obukhovskiĭ, Topological methods in the fixed point theory of multivalued mappings, Russian Math. Surveys 35 (1980), 65-143.
  • [4] Yu. G. Borisovich, V. G. Zvyagin and Yu. I. Sapronov, Nonlinear Fredholm mappings and Leray-Schauder theory, ibid. 32 (1977), 3-54.
  • [5] K. Gęba, Algebraic topology methods in the theory of compact fields in Banach spaces, Fund. Math. 46 (1964), 177-209.
  • [6] K. Gęba, I. Massabò and A. Vignoli, Generalized topological degree and bifurcation, in: Nonlinear Functional Analysis and its Applications (Maratea, 1985), Reidel, 1986, 55-73.
  • [7] S. Goldberg, Unbounded Linear Operators. Theory and Applications, McGraw-Hill, 1966.
  • [8] L. Górniewicz, Homological methods in fixed-point theory of multi-valued maps, Dissertationes Math. 129 (1976).
  • [9] L. Górniewicz and W. Kryszewski, Bifurcation invariants for acyclic mappings, Rep. Math. Phys. 31 (1992), 217-239.
  • [10] J. Izé, I. Massabò and A. Vignoli, Degree theory for equivariant maps I, Trans. Amer. Math. Soc. 315 (1989), 433-510.
  • [11] J. L. Kelley, General Topology, Van Nostrand, New York, 1955.
  • [12] W. Kryszewski, Homotopy properties of set-valued mappings, Wyd. Uniwersytetu Mikołaja Kopernika, Toruń, 1997.
  • [13] W. Kryszewski, Topological and approximation methods in the degree theory of set-valued maps, Dissertationes Math. 336 (1994).
  • [14] W. Kryszewski, The fixed-point index for the class of compositions of acyclic set-valued maps on ANR's, Bull. Sci. Math. 120 (1996), 129-151.
  • [15] W. Kryszewski, Remarks to the Vietoris Theorem, Topol. Methods Nonlinear Anal. 8 (1996), 383-405.
  • [16] R. C. Lacher, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc. 83 (1977), 336-552.
  • [17] J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS Regional Conf. Ser. in Math. 40, Amer. Math. Soc., Providence, 1979.
  • [18] T. Pruszko, Some applications of the topological degree theory to multi-valued boundary value problems, Dissertationes Math. 229 (1984).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv75z2p143bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.