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Modern approach to the theory of topological characteristics of nonlinear operators I

Part of the Lecture Notes in Mathematics book series (LNM,volume 1334)

Keywords

  • Banach Space
  • Vector Field
  • Multivalued Mapping
  • Homotopic Class
  • Topological Characteristic

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Dmitrienko V.T., Zvyagin V.G. Homotopic classification of a single class of continuous mappings.-Mat. zametki, 1982, 31, issue 5, p. 801–812.(in Russian)

    MathSciNet  MATH  Google Scholar 

  2. Zvyagin V.G. To the theory of generalized condensing perturbations of continuous mappings.-In: Topological and geometrical methods in mathematical physics. Voronezh: VGU, 1983, p.42–62. (in Russian)

    Google Scholar 

  3. Dmitrienko V.T., Zvyagin V.G. Homotopic classification of generalized condensing perturbations of mappings.-IV Tiraspol' Symposium on General Topology and its Applications. Kishinev: Shtiintsa, 1979, p.32–33. (in Russian)

    Google Scholar 

  4. Dmitrienko V.T. Homotopic classification of a single class of multi-valued mappings.-Voronezh University, Voronezh, 1980, Deposited in VINITI, No.2091-80 Dep.(in Russian)

    Google Scholar 

  5. Borisovich Yu.G., Zvyagin V.G. Perturbations of nonlinear Fredholm operators and their application to boundary value problems.-In:General theory of boundary problems, Kiev: Nauk.dumka, 1983, p.35–43.

    Google Scholar 

  6. Borisovich Yu.G. To the theory of topological degree of nonlinear Fredholm mappings perturbed by a multi-valued operator. Voronezh University, Voronezh, 1980. Deposited in VINITI No.5026-80 Dep., 7p.

    Google Scholar 

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

    Google Scholar 

  8. Borisovich Yu.G. Topology and nonlinear functional analysis.-Uspekhi mat. nauk, 1979, 34, issue 6, p.14–22. (in Russian)

    MathSciNet  MATH  Google Scholar 

  9. Borisovich Yu.G. On topological methods in the problem of solvability of non-linear equations. Trudy.Leningr. mezhdunar. topol. konf., 23–27 August, 1982, L.: Nauka, 1983, p.39–49. (in Russian)

    Google Scholar 

  10. Borisovich Yu.G. On topological characteristics of nonlinear Fredholm operators and their perturbations.-In: Optimal management. Geometry and analysis. Tezisy dokl. vsesoyuznoi shkoly, Kemerovo, izdvo Kem.GU, 1968, p.68. (in Russian)

    Google Scholar 

  11. Borisovich Yu.G. Global analysis and solvability of nonlinear boundary value problems.-In: Application of functional methods of the function theory to the problems of mathematical physics. Tezisy dokl. IX Sovetsko-Chekhoslovatskogo soveshchaniya.-Donetsk, 1986, p.17. (in Russian)

    Google Scholar 

  12. Borisovich Yu.G., Ratiner N.M. On new constructions of topological characteristics of nonlinear Fredholm operators. In: XI All-Union Seminar on the Operator Theory in Functional Spaces. Tezisy dokl.p.I, Chelyabinsk, 1986, p.17. (in Russian)

    Google Scholar 

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

    Google Scholar 

  14. Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskii V.V. Topological methods in the theory of fixed points of multivalued mappings.-Uspekhi mat. nauk, 1980, v.35, issue I, p.59–126. (In Russian)

    MathSciNet  Google Scholar 

  15. Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskii V.V. Multivalued mappings.-In: Results of science and technology. Math. analysis, Moscow, 1982, v.19, p.127–230. (In Russian).

    MathSciNet  Google Scholar 

  16. Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskii V.V. Multivalued analysis and operator inclusions.-In: Results of science and Technology. Modern problems of mathematics. Latest achievements., Moscow, 1986, v.29, p.127–230. (IN Russian).

    Google Scholar 

  17. Borisovich Yu.G., Sapronov Yu.I. To the topological theory of compact contracted-mappings.-In: Trudy seminara po funkts.analizu, Voronezh, VGU, 1969, issue 12, p.43–68. (In Russian).

    Google Scholar 

  18. Borisovich Yu.G., Sapronov Yu.I. To the topological theory of condensing operators.-DAN SSSR, 1968, 183, No.1, p.18–20. (In Russian).

    MATH  Google Scholar 

  19. Sapronov Yu.I. To the algebraic index theory.-Trudy seminara po funkts.analizu, Voronezh, VGU, 1969, issue 12, p.143–154. (In Russian)

    Google Scholar 

  20. Sapronov Yu.I. To the homotopic classification of condensing mappings.-Trudy matem. fak. VGU, Voronezh, VGU, 1972, issue 6, p.78–80. (In Russian).

    Google Scholar 

  21. Sapronov Yu.I. To the degree theory of nonlinear Fredholm mappings.-In: Trudy NIIM, Voronezh, VGU, 1973, issue XI, p.92–101. (In Russian).

    Google Scholar 

  22. Borisovich Yu.G., Zvyagin V.G., Sapronov Yu.I. Nonlinear Fredholm mappings and Leray-Schauder theory.-Uspekhi mat.nauk, 1977, 32, No.4, p.3–54. (In Russian).

    MathSciNet  MATH  Google Scholar 

  23. Borisovich Yu.G., Zvyagin V.G. On a single topological principle of solvability of equations with Fredholm operators.-Dokl.AN USSR, 1976, ser.A, No.3 (In Russian).

    Google Scholar 

  24. Sadovskii B.N. Limiting compact and condensing operators.-Uspekhi matem-nauk, 27, issue I(1972), p.81–146. (In Russian).

    MathSciNet  Google Scholar 

  25. Akhmerov R.R., Kamenskii M.I., Potapov A.S., Sadovskii B.N. Condensing operators.-Itogi nauki i tekhniki, v.18, Moscow, VINITI, 1980, p.185–250. (In Russian).

    Google Scholar 

  26. Krasnosel'skii M.A., Zabreiko P.P. Geometrical methods of nonlinear analysis, Moscow, Nauka, 1975. (In Russian).

    Google Scholar 

  27. Akhmerov R.R., Kamenskii M.I., Potapov A.S., Rodkina A.E., Sadovskii B.N. Measures of non-compactness and condensing operators.-Novosibirks, 1986.-265 p. (In Russian).

    Google Scholar 

  28. Leray J. Sur les equations et les transformations.-Jour. de Math. Pures et Appl. 9e Serie, 24(1945); pp.201–248.

    MathSciNet  MATH  Google Scholar 

  29. Borisovich Yu.G. On one application of the notion of vector field rotation.-Dokl.AN SSSR, 1963, 153, No.I, p.12–15. (In Russian).

    Google Scholar 

  30. Borisovich Yu.G. On relative rotation of compact vector fields in linear spaces.-In: Trudy seminara po funkts. analizu, Voronezh, VGU, 1969, issue 12, p.3–27. (In Russian).

    Google Scholar 

  31. Sadovskii B.N. On measures of non-compactness and condensing operators.-IN: Problemy matem. analiza slozhnykh sistem, Voronezh, VGU, 1968, issue 2. (In Russian).

    Google Scholar 

  32. Nussbaum R.D. The fixed point index and asymptotic fixed-point theorem for k-set-contractions.-Bull. Amer. Math. Soc., 1969, v.75, No.3, p.490–495.

    CrossRef  MathSciNet  MATH  Google Scholar 

  33. Nussbaum R.D. The fixed point index for local condensing maps.-Ann. mat. pura ed appl., 1971, t.89, p.217–258.

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. Nussbaum R.D. Degree theory for local condensing mans.-J. Math. Analysis and Applic., 1972, v.37, No.3, p.741–766.

    CrossRef  MathSciNet  MATH  Google Scholar 

  35. Zabreiko P.P., Krasnosel'skii M.A., Strygin V.V. On the principles of rotation invariance.-Izv. vuzov, Matematika, 1972, v.5(120), p.51–57. (In Russian).

    MathSciNet  Google Scholar 

  36. Obukhovskii V.V. On some principles of fixed point for multivalued condensing operators. — In: Trudy mat. fak., Voronezh, VGU, 1971, Issue 4, p.70–79. (In Russian).

    Google Scholar 

  37. Obukhovskii V.V., Gorokhov E.V. To the definition of rotation of a single class of compact contracted multivalued vector fields.-Trudy mat. fak., Voronezh, VGU, 1974, issue 12, p.45–52. (In Russian).

    Google Scholar 

  38. Borisovich Yu.G., Obukhovskii V.V. Homotopic properties, theory of rotation and theorems on fixed point for a single class of noncompact multivalued mappings. Voronezh, 1980. Deposited in VINITI, No.5033-80 Dep., 34 p. (In Russian).

    Google Scholar 

  39. Evert J. Homotopical properties and the Topological Degree for r-contraction Vector Fields.-Bull. Acad. Polon. Sci., 1980, 28, No.5–6, p.273–274.

    MathSciNet  Google Scholar 

  40. Izrailevich Ya.A. On the notion of relative rotation of multivalued vector field.-Trudy seminara po funkts. analizu, Voronezh, VGU, 1969, issue 12, p.111–115. (In Russian).

    Google Scholar 

  41. Borisovich Yu.G. Relative rotation of compact vector fields and Lefshetz number.-Trudy seminara po funkts. analizu, Voronezh, VGU, 1969, issue 12, p.28–42 (In Russian).

    Google Scholar 

  42. Vulikh-B.Z. Introduction into the theory of semi-ordered spaces.-Moscow, 1961, 407 p. (In Russian).

    Google Scholar 

  43. Smale S. An infinite dimensional version of Sard's theorems.-Amer. J. Math., 1965, 87, p.861–866.

    CrossRef  MathSciNet  MATH  Google Scholar 

  44. Elworthy K.D., Tromba A.J. Differential structures and Fredholm maps on Banach manifolds.-Proc. Sympos. Pure Math., AMS, 1970, 15, p.45–94.

    CrossRef  MathSciNet  MATH  Google Scholar 

  45. Shvarts A.S. Homotopic topology of Banach spaces.-Dokl. AN SSSR, 154 (1964), p.61–63. (In Russian).

    MathSciNet  MATH  Google Scholar 

  46. Nirenberg L. Generalized degree and nonlinear problems.-Contribution to Nonlinear Functional analysis.-Acad. Press, New York/London, 1971, p.1–9.

    CrossRef  Google Scholar 

  47. Zvyagin V.G. On the existence of continuous branch of eigenfunctions of nonlinear elliptic boundary value problem.-Differentsial'nye uravneniya, 1977, issue 8, p.1524–1527. (In Russian).

    Google Scholar 

  48. Zvyagin V.G. On one topological method of investigation of boundary value problems, nonlinear with respect to highest derivative.-In: Granichnye zadachi matematicheskoi fiziki. Kiev: Nauk. dumka, 1981, p.35–37. (In Russian).

    Google Scholar 

  49. Skrypnik I.V. Nonlinear elliptic equations of highest order.-Kiev:Nauk.dumka, 1973 (in Russian).

    MATH  Google Scholar 

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Borisovich, Y.G. (1988). Modern approach to the theory of topological characteristics of nonlinear operators I. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A. (eds) Global Analysis — Studies and Applications III. Lecture Notes in Mathematics, vol 1334. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080430

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  • DOI: https://doi.org/10.1007/BFb0080430

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