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Topological characteristics of infinite - dimensional mappings and the theory of fixed points and coincidences

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Topological Fixed Point Theory and Applications

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References

  1. Borisovich Yu.G., Zvyagin V.G., Sapronov Yu.I. Nonlinear Fredholm mappings and Leray-Schauder theory // Uspekhi mat. nauk. 32:4(1977), 3–54 (in Russian).

    MathSciNet  MATH  Google Scholar 

  2. Krasnosel'skii M.A., Zabreiko P.P. Geometrical methods of nonlinear analysis, Berlin, Heidelberg, New York, Tokyo, Springer, 1984.

    Book  Google Scholar 

  3. Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskii V.V. Multivalued mappings // Itogi nauki i tekhn. VINITI. Matematicheskii analiz. 19(1982), 127–230 (in Russian).

    MathSciNet  Google Scholar 

  4. Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskii V.V. Multivalued analysis and operator inclusions // Itogi nauki i tekhn. VINITI. sovremennye problemy matematiki. Noveishie dostizheniya. 29(1986), 151–211 (in Russian).

    MathSciNet  Google Scholar 

  5. Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskii V.V. On new results in the theory of multivalued mappings. I. Topological characteristics and solvability of operator relations// Itogi nauki i tekhn. VINITI. Matematicheskii analiz. 251987, 121–195 (in Russian).

    MathSciNet  MATH  Google Scholar 

  6. Borisovich Yu.G., Zvyagin V.G. On one topological principle of solvability of equations with Fredholm operators // Dokl. AN USSR, 1976, ser.A, No.3, 204–206 (in Russian).

    Google Scholar 

  7. Ratiner N.M. To the degree theory of Fredholm mappings of non-negative index, Voronezh University, Voronezh, 1981, dep. VINITI, No. 1493–81, 31p. (in Russian).

    Google Scholar 

  8. Borisovich Yu.G., Sapronov Yu.I. To the theory of nonlinear Fredholm mappings // Trudy VIII letnei matematicheskoi shkoly, Kiev, Institut matematiki AN USSR, 1971, 128–163 (in Russian).

    Google Scholar 

  9. Skubachevskii A.L. Elliptic problems with non-local conditions in the neighbouhood of the boundary // Matem.sb., 129:2(1986), 279–302 (in Russian).

    MathSciNet  Google Scholar 

  10. Zvyagin V.G., Dmitrienko V.T. Homotopic classification of one class of continuous mappings // Mat.zametki. 31:5(1982), 801–812 (in Russian).

    MathSciNet  MATH  Google Scholar 

  11. Borisovich Yu.G. Topology and nonlinear functional analysis // Uspekhi mat.nauk, 34:6(1979), 14–22 (in Russian).

    MathSciNet  MATH  Google Scholar 

  12. Zvyagin V.G. To the theory of generalized condensing perturbations of continuous mappings // Topological and geometrical methods in mathematical physics.-Voronezh: Izd-vo VGU, 1983, 42–62 (in Russian) (English translation in: L.N. in Math., vol.1108).

    Google Scholar 

  13. Borisovich Yu.G. On topological methods in the problem of solvability of nonlinear equations. Tr. Leningr. mezhdunar. topol. konf., 23–27 August, 1982, Leningrad: Nauka, 1983, 39–49 (in Russian).

    MATH  Google Scholar 

  14. Borisovich Yu.G. On the solvability of nonlinear equations with Fredholm operators // Geometry and topology in global nonlinear problems.-Voronezh, VGU, 1984, 3–22 (in Russian, English translation in: L.N. in Math. vol. 1108).

    Google Scholar 

  15. Borisovich Yu.G. Modern approach to the theory of topological characteristics of nonlinear operators. I. // Geometry and the theory of singularities in nonlinear equations, Voronezh, VGU, 1987, 24–46 (in Russian, English translation to appear in L.N in Math.).

    Google Scholar 

  16. Borisovich Yu.G. Modern approach to the theory of topological characteristics of nonlinear operators, II // Global analysis and nonlinear equations.-Voronezh, VGU, 1988 (in Russian).

    Google Scholar 

  17. Lecture Notes in Math. 1108, 1214, Global Analysis—Studies and Applications, I, II, Ed. by Yu.G.Borisovich, Yu.E.Gliklikh, Springer-Verlag, 1984, 1986.

    Google Scholar 

  18. Borisovich Yu.G., Sapronov Yu.I. To the topological theory of compact contracted mappings // Trudy seminara po funkts. analizu, Voronezh, VGU, 1969, vyp.12, 43–68 (in Russian).

    Google Scholar 

  19. Sapronov Yu.I. Breach of spherical symmetry in nonlinear variational problems // Analiz na mnogoobraziyakh i differentisial'nye uraveniya, Voronezh, VGU, 1986, 88–111 (in Russian).

    Google Scholar 

  20. Sapronov Yu.I. On two-mode bifurcations of solutions to Karman equation // VI Republican conference “Nonlinear problems of mathematical physics”, Donetsk, tez, 1987, 132 (in Russian).

    Google Scholar 

  21. Sapronov Yu.I. Multidimensional sleeping tops // Global analysis and mathematical physics, Voronezh, VGU, 1987, 95–109 (in Russian, English translation to appear in L.N. in Math.).

    Google Scholar 

  22. Borisovich A.Yu. One geometrical application of the thoerem on a simple bifurcation point // Application of topology in modern analysis, Voronezh, VGU, 1985, 172–174 (in Russian).

    Google Scholar 

  23. Borisovich A.Yu. Reduction of the problem on bifurcation of minimal surfaces to operator equations and the search of bifurcations from catenoid, helicoid, surfaces of Scherk and Enneper // Uspekhi mat. nauk, 41:5(1986), 165–166 (in Russian).

    MathSciNet  MATH  Google Scholar 

  24. Borisovich A.Yu. Plateau operator and bifurcation of two-dimensional surfaces // Global analysis and mathematical physics, Voronezh, VGU, 1987, 142–154 (in Russian, English translation to appear in L.N. in Math.).

    Google Scholar 

  25. Tromba A.J. Degree theory on oriented infinite dimensional varieties and the Morse number of minimal surfaces spanning a curve in R n. Part I: n ≥ 4 // Transactions of the Amer. Math. Soc. 290:1(1985), 385–412.

    MathSciNet  MATH  Google Scholar 

  26. Zvyagin V.G. On the number of solutions to some boundary problems // Global analysis and mathematical physics, Voronezh, VGU, 1987, 60–72 (in Russian, English translation to appear in L.N. in Math.).

    Google Scholar 

  27. Borisovich Yu.G., Gel'man B.D., Myshkis L.D., Obukhovskii V.V. Topological methods in the theory of fixed points of multivalued mappings // Uspekhi mat. nauk. 35:1(1980), 59–126 (in Russian).

    MathSciNet  Google Scholar 

  28. Gel'man B.D. To the fixed points theorem of Kakutani type for multivalued mappings // Global analysis and nonlinear equations, Voronezh, VGU, 1988 (in Russian).

    Google Scholar 

  29. Bliznyakov N.M. Cauchy indices and singular point index of a vector field. // Application of topology in modern analysis-Voronezh, VGU, 1985, 3–21 (in Russian, English translation in Lecture Notes in Math., vol. 1214).

    Google Scholar 

  30. Izrailevich Ya.A. To the singular points theory of iterative processes // Geometry and the theory of singularities in nonlinear equations, Voronezh, VGU, 1987, 146–151 (in Russian, English translation in Lecture Notes in Math., in print).

    Google Scholar 

  31. Borisovich Yu.G., Fomenko T.N. Homological methods in the theory of periodic and equivariant mappings // Global analysis and mathematical physics, Voronezh, VGU, 1987, 3–25 (in Russian, English translation to appear in L.N. in Math.).

    Google Scholar 

  32. Shchelokova T.N. To the calculation problem of the degree of an equivariant mapping // Sibirskii mat. zhurn, 19:2(1978), 426–435 (in Russian).

    MATH  Google Scholar 

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Boju Jiang

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© 1989 Springer-Verlag

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Borisovich, Y.G. (1989). Topological characteristics of infinite - dimensional mappings and the theory of fixed points and coincidences. In: Jiang, B. (eds) Topological Fixed Point Theory and Applications. Lecture Notes in Mathematics, vol 1411. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086437

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  • DOI: https://doi.org/10.1007/BFb0086437

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