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Uspekhi Mat. Nauk, 1977, Volume 32, Issue 4(196), Pages 3–54 (Mi umn3218)  

This article is cited in 53 scientific papers (total in 53 papers)

Non-linear Fredholm maps and the Leray–Schauder theory

Yu. G. Borisovich, V. G. Zvyagin, Yu. I. Sapronov


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English version:
Russian Mathematical Surveys, 1977, 32:4, 1–54

Bibliographic databases:

UDC: 517.43+513.731+529.4
MSC: 47H09, 47A53, 47H11, 47H30
Received: 15.01.1976

Citation: Yu. G. Borisovich, V. G. Zvyagin, Yu. I. Sapronov, “Non-linear Fredholm maps and the Leray–Schauder theory”, Uspekhi Mat. Nauk, 32:4(196) (1977), 3–54; Russian Math. Surveys, 32:4 (1977), 1–54

Citation in format AMSBIB
\Bibitem{BorZvySap77}
\by Yu.~G.~Borisovich, V.~G.~Zvyagin, Yu.~I.~Sapronov
\paper Non-linear Fredholm maps and the Leray--Schauder theory
\jour Uspekhi Mat. Nauk
\yr 1977
\vol 32
\issue 4(196)
\pages 3--54
\mathnet{http://mi.mathnet.ru/umn3218}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=464282}
\zmath{https://zbmath.org/?q=an:0358.58004|0383.58002}
\transl
\jour Russian Math. Surveys
\yr 1977
\vol 32
\issue 4
\pages 1--54
\crossref{https://doi.org/10.1070/RM1977v032n04ABEH001638}


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    This publication is cited in the following articles:
    1. Yu. G. Borisovich, “Topology and non-linear functional analysis”, Russian Math. Surveys, 34:6 (1979), 14–23  mathnet  crossref  mathscinet  zmath
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    3. Volker Aurich, “Bifurcation of the solutions of holomorphic Fredholm equations and complex analytic graph theorems”, Nonlinear Analysis: Theory, Methods & Applications, 6:6 (1982), 599  crossref
    4. J. P. Fink, W. C. Rheinboldt, “On the Error Behavior of the Reduced Basis Technique for Nonlinear Finite Element Approximations”, Z angew Math Mech, 63:1 (1983), 21  crossref  mathscinet  zmath  isi
    5. James P. Fink, Werner C. Rheinboldt, “On the Discretization Error of Parametrized Nonlinear Equations”, SIAM J Numer Anal, 20:4 (1983), 732  crossref  mathscinet  zmath  isi
    6. A. B. Antonevich, “On two methods of studying the invertibility of operators in $C^*$-algebras induced by dynamical systems”, Math. USSR-Sb., 52:1 (1985), 1–20  mathnet  crossref  mathscinet  zmath
    7. M. I. Vishik, S. B. Kuksin, “Perturbations of quasilinear elliptic equations and Fredholm manifolds”, Math. USSR-Sb., 58:1 (1987), 223–243  mathnet  crossref  mathscinet  zmath
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    9. A. A. Irmatov, “Topology of the space of Fredholm operators and invariants of non-linear Fredholm maps”, Russian Math. Surveys, 45:1 (1990), 205–206  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. V. G. Zvyagin, “The degree of Fredholm maps equivariant with respect to the actions of the circle and the torus”, Russian Math. Surveys, 45:2 (1990), 229–230  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. V. G. Zvyagin, “On the oriented degree of a certain class of perturbations of Fredholm mappings, and on bifurcation of solutions of a nonlinear boundary value problem with noncompact perturbations”, Math. USSR-Sb., 74:2 (1993), 487–512  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. G. A. Sviridyuk, “On the general theory of operator semigroups”, Russian Math. Surveys, 49:4 (1994), 45–74  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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    14. P.T. Church, J.G. Timourian, “Oriented global fold maps in differential and integral equations”, Nonlinear Analysis: Theory, Methods & Applications, 26:1 (1996), 9  crossref
    15. Borisovich Y.G., “A generalized degree of multivalued mappings and its applications to nonlinear problems”, Nonlinear Analysis-Theory Methods & Applications, 30:1 (1997), 101–109  crossref  mathscinet  zmath  isi  elib
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    19. G. A. Sviridyuk, T. G. Sukacheva, “On the solvability of a nonstationary problem describing the dynamics of an incompressible viscoelastic fluid”, Math. Notes, 63:3 (1998), 388–395  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. T. G. Sukacheva, “On the solvability of a nonstationary problem of the dynamics of an incompressible viscoelastic Kelvin–Voigt fluid of nonzero grade”, Russian Math. (Iz. VUZ), 42:3 (1998), 44–51  mathnet  mathscinet  zmath  elib
    21. Yu. I. Sapronov, S. L. Tsarev, “Global comparison of finite-dimensional reduction schemes in smooth variational problems”, Math. Notes, 67:5 (2000), 631–638  mathnet  crossref  crossref  mathscinet  zmath  isi
    22. V. S. Klimov, “Infinite-dimensional version of the Poincare–Hopf theorem and homological characteristics of functionals”, Sb. Math., 192:1 (2001), 49–64  mathnet  crossref  crossref  mathscinet  zmath  isi
    23. V. G. Zvyagin, V. T. Dmitrienko, Z. Kukharski, “Topological characterization of the solution set of Fredholm equations with $f$-compactly contractive perturbations and its applications”, Russian Math. (Iz. VUZ), 45:1 (2001), 33–45  mathnet  mathscinet  zmath
    24. T. G. Sukacheva, O. P. Matveeva, “Spline approximations of the solution of a singular integro-differential equation”, Russian Math. (Iz. VUZ), 45:11 (2001), 44–51  mathnet  mathscinet  zmath
    25. T. G. Sukacheva, “Kvazistatsionarnye polutraektorii odnogo klassa polulineinykh uravnenii sobolevskogo tipa”, Vestnik ChelGU, 2002, no. 6, 71–85  mathnet
    26. T. G. Sukacheva, M. N. Daugavet, “Linearizovannaya model dvizheniya vyazkouprugoi neszhimaemoi zhidkosti Kelvina–Foigta nenulevogo poryadka”, Sib. zhurn. industr. matem., 6:4 (2003), 111–118  mathnet  mathscinet  zmath
    27. Yu. G. Borisovich, A. A. Demchenko, “On the construction of a degree theory for completely continuous and Fredholm sections of Banach vector bundles”, Russian Math. (Iz. VUZ), 47:8 (2003), 1–4  mathnet  mathscinet  zmath  elib
    28. B. M. Darinskii, Yu. I. Sapronov, S. L. Tsarev, “Bifurcations of extremals of Fredholm functionals”, Journal of Mathematical Sciences, 145:6 (2007), 5311–5453  mathnet  crossref  mathscinet  zmath  elib
    29. Patrick J. Rabier, “Superlinear convolution equations in”, Nonlinear Analysis: Theory, Methods & Applications, 64:10 (2006), 2279  crossref
    30. Ya. M. Dymarskii, “Manifold Method in Eigenvector Theory of Nonlinear Operators”, Journal of Mathematical Sciences, 154:5 (2008), 655–815  mathnet  crossref  mathscinet  zmath  elib
    31. I. V. Kolesnikova, “Dvukhmodovye vetvleniya ekstremalei gladkikh funktsionalov v tochkakh minimuma s odnorodnymi osobennostyami shestogo poryadka”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 9:2 (2009), 25–30  mathnet  crossref  elib
    32. Kolesnikova I.V., Sapronov Yu.I., “Dvukhmodovye vetvleniya segnetoelektricheskikh faz kristalla vblizi kriticheskoi fazy s odnorodnoi osobennostyu shestogo poryadka”, Vestn. Chelyabinskogo gos. un-ta, 2009, no. 20, 37–47  elib
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    34. Darinskii B.M., Kolesnikova I.V., Sapronov Yu.I., “Vetvlenie segnetoelektricheskikh faz neodnorodnogo kristalla vblizi kriticheskoi fazy s trekhmernoi osobennostyu shestogo poryadka”, Vestn. Voronezhskogo gos. un-ta. Ser.: Fiz. Matem., 2009, no. 1, 101–107  elib
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    37. T. G. Sukacheva, “Zadacha termokonvektsii dlya linearizovannoi modeli dvizheniya neszhimaemoi vyazkouprugoi zhidkosti”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2010, no. 5, 83–93  mathnet
    38. Patrick Bernard, “On the Number of Mather Measures of Lagrangian Systems”, Arch Rational Mech Anal, 197:3 (2010), 1011  crossref
    39. Kostina T.I., “Nelokalnoe vychislenie klyuchevykh funktsii v zadache o periodicheskikh resheniyakh variatsionnykh uravnenii”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2011, no. 1, 181–186  elib
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    41. O. P. Matveeva, T. G. Sukacheva, “Obobschennaya odnorodnaya model termokonvektsii neszhimaemoi vyazkouprugoi zhidkosti”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 8, 62–69  mathnet
    42. V. G. Zvyagin, N. M. Ratiner, “Oriented degree of Fredholm maps: finite-dimensional reduction method”, Journal of Mathematical Sciences, 204:5 (2015), 543–714  mathnet  crossref  mathscinet
    43. Nguyen Van Loi, Valeri Obukhovskii, Jen-Chih Yao, “A Bifurcation of Solutions of Nonlinear Fredholm Inclusions Involving CJ-Multimaps with Applications to Feedback Control Systems”, Set-Valued Var. Anal, 2012  crossref
    44. Dzhasim M.D., Efendiev A.R., Karpova A.P., Kostin D.V., “Amplitudnaya optimizatsiya tsiklov, bifurtsiruyuschikh pri nalichii kratnykh rezonansov”, Vestnik dagestanskogo gosudarstvennogo universiteta, 2012, no. 1, 99–105  elib
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    49. J. Pejsachowicz, “The index bundle and bifurcation from infinity of solutions of nonlinear elliptic boundary value problems”, J. Fixed Point Theory Appl, 2015  crossref
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    53. A. O. Kondyukov, T. G. Sukacheva, “Fazovoe prostranstvo pervoi nachalno-kraevoi zadachi dlya sistemy Oskolkova vysshego poryadka”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:4 (2018), 67–77  mathnet  crossref  elib
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