PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Solving equations by topological methods

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in diffrential equations.
Rocznik
Strony
195--225
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
  • Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, ul. Chopina 12/8, 87-100 Toruń, Poland, gorn@mat.uni.torun.pl
Bibliografia
  • [M-1] Agarwal R. P., Meehan M., O'Regan D.: Fixed Point Theory and Applications. Cambridge University Press, Cambridge: 2001
  • [M-2] Andres J., Górniewicz L.: Topological Fixed Point Principles for Boundary Value Problems. Dordrecht, Kluwer Acad. Publ. 2003
  • [M-3] Borsuk K.: Theory of Retracts. Monografie Matematyczne, vol. 44, Warsaw PWN 1967
  • [M-4] K. Borsuk Theory of Shape. Monografie Matematyczne, vol. 59, Warsaw PWN 1975
  • [M-5] Brown R.F.: The Lefschetz Fixed Point Theorem. Glenview, Scott, Foresman and Co., 1971
  • [M-6] Brown R. F.: A Topological Introduction to Nonlinear Analysis. Boston, Birkhauser 1993
  • [M-7] Dold A.: Lectures on Algebraic Topology. Berlin, Springer, 1972
  • [M-8] Dugundji J., Granas A.: Fixed Point Theory. I Monograf. Mat., vol. 61, Warsaw, PWN 1982
  • [M-9] Goebel K.: Coincise Course on Fixed Point Theorems. Yokohama, Yokohama Publishers 2002
  • [M-10] Górniewicz L.: Topological Fixed Point Theory of Multivalued Mappings. Klu-wer, Dordrecht 1999
  • [M-11] Krasnosel'skii M. A.: Topological Methods in the Theory of Nonlinear Integral Equations. Gos. Izdat. Tehn.-Trov. Lit. Moscow 1956 (in Russian); Oxford, Pergamon Press 1963 (English translation)
  • [M-12] Lloyd N.G.: Degree Theory. Cambridge, Cambridge Univ. Press 1978
  • [M-13] Rothe E. H.: Introduction to Various Aspects of Degree Theory in Banach Spaces. Mathematical Surveys and Monographs, vol. 23, AMS, Providence, R.I. 1986
  • [M-14] Spanier E.H.: Algebraic Topology. New York, McGraw-Hill 1966
  • [M-15] Brown R. F., Furi M., Górniewicz L., Jiang B.: Handbook of Topological Fixed Point Theory. Dordrecht, Kluwer (to appear).
  • [1] Andres J., Jezierski J., Górniewicz L.: Relative versions of the multivalued Lefschetz and Nielsen theorems and their application to admissible semi-flows. Topol. Methods Nonlinear Anal. 16 (2000), 73-92; Periodic points of multi­valued mappings with applications to differential inclusions. Top. and Appl. 127 (2003), 447-472
  • [2] Bowszyc C.: Fixed point theorem for the pairs of spaces. Bull. Polish Acad. Sci. Math. 16 (1968), 845-851; 17 (1969), 367-372; On the Euler-Pomcaire characteristic of a map and the existence of periodic points. Bull. Acad. Polon. Sci. 17 (1969), 367-372
  • [3] Fournier G.: Generalisations du theoreme de Lefschetz pour des espaces non-compacts I, II, III. Bull. Acad. Polon. Sci. 23 (1975), 693-699, 701-706, 707-711
  • [4] Fournier G., Górniewicz L.: The Lefschetz fixed point theorem for some non-compact multivalued maps. Fund. Math. 94 (1977) 245-254; The Lefschetz fixed point theorem for multivalued maps of non-metrizable spaces. Fund. Math. 92 (1976), 213-222; 94 (1977), 245-254
  • [5] Fournier G., Violette D.: A fixed point index for compositions of acyclic multivalued maps in Banach spaces. The MSRI-Korea Publications 1 (1966), 139-158; Ann. Sci. Math. Quebec 22 (1998), 225-244
  • [6] Górniewicz L.: Homological methods in fixed point theory of multivalued map­pings. Dissertationes Math. 129 (1976), 1-71; On the Lefschetz fixed point theorem. Math. Slovaca 52 (2002) 2; Topological structure of solutions sets, current results. Archivum Math. 36 (2000), 343-382
  • [7] Górniewicz L., Granas A.: On the theorem of C. Bowszyc concerning the rela­tive version of the Lefschetz fixed point theorem. Bull. Inst. Math. Academića Sinica 12 (1975), 137-142
  • [8] Granas A.: Generalizing the Hopf-Lefschetz fixed point theorem for non-compact ANR's. Symp. Inf. Dim. Topol. Baton-Rouge (1967), 119-130
  • [9] Granas A.: The Leray-Schauder index and the fixed point theory for arbitrary ANR's. Bull. Soc. Math. France 100 (1972) 209-228
  • [10] Kryszewski W.: The Lefschetz type theorem for a class of noncompact mapping. Rend. del. Circolo Matemat. di Palermo, Ser. II 14 (1987), 365-384
  • [11] Nussbaum R.: Generalizing the fixed point index. Math. Ann. 228 (1979) 259-278; Springer, Lecture Notes Math. 1537 (1991)
  • [12] Pastor D.: A remark on generalized compact maps. Studies Univ. Zilina 13 (2001), 147-155
  • [13] Srzednicki R.: Generalized Lefschetz theorem and fixed point index formula. Topol. Appl. 81 (1997), 207-224
  • [14] Seda V.: On condensing discrete dynamical systems. Math. Bohemica 11 (2002), 275-289
  • [15] Thompson R. B.: A unified approach to local and global fixed point indices. Adv. Math. 3 (1969), 1-71
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0003-0045
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.