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Uspekhi Mat. Nauk, 1962, Volume 17, Issue 2(104), Pages 13–75 (Mi umn6481)  

This article is cited in 41 scientific papers (total in 42 papers)

The methods of Lyapunov and Schmidt in the theory of non-linear equations and their further development

M. M. Vainberg, V. A. Trenogin


Full text: PDF file (6029 kB)

English version:
Russian Mathematical Surveys, 1962, 17:2, 1–60

Bibliographic databases:

MSC: 45G05, 45G15, 47J07
Received: 09.05.1961

Citation: M. M. Vainberg, V. A. Trenogin, “The methods of Lyapunov and Schmidt in the theory of non-linear equations and their further development”, Uspekhi Mat. Nauk, 17:2(104) (1962), 13–75; Russian Math. Surveys, 17:2 (1962), 1–60

Citation in format AMSBIB
\Bibitem{VaiTre62}
\by M.~M.~Vainberg, V.~A.~Trenogin
\paper The methods of Lyapunov and Schmidt in the theory of non-linear equations and their further development
\jour Uspekhi Mat. Nauk
\yr 1962
\vol 17
\issue 2(104)
\pages 13--75
\mathnet{http://mi.mathnet.ru/umn6481}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=154113}
\zmath{https://zbmath.org/?q=an:0117.31904}
\transl
\jour Russian Math. Surveys
\yr 1962
\vol 17
\issue 2
\pages 1--60
\crossref{https://doi.org/10.1070/RM1962v017n02ABEH001127}


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    Citing articles on Google Scholar: Russian citations, English citations
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    1. P. G. Aizengendler, “Nekotorye voprosy teorii vetvleniya reshenii nelineinykh uravnenii”, UMN, 21:1(127) (1966), 182–183  mathnet
    2. Stephen Bancroft, Jack K Hale, Daniel Sweet, “Alternative problems for nonlinear functional equations”, Journal of Differential Equations, 4:1 (1968), 40  crossref
    3. Helmut Pachale, “Eine Bemerkung zur Theorie der nichtlinearen Gleichungen”, Arch Math, 20:3 (1969), 279  crossref  mathscinet
    4. Ivar Stakgold, “Branching of Solutions of Nonlinear Equations”, SIAM Rev, 13:3 (1971), 289  crossref  mathscinet  zmath
    5. Edward T. Dean, Paul L. Chambré, “On the Bifurcation of Solutions of the Nonlinear Eigenvalue Problem $Lu + \lambda b(x)u = g(x,u)$”, SIAM J Appl Math, 20:4 (1971), 722  crossref  mathscinet  zmath
    6. DAHSOONG Yü, “Domain of stability for a class of non-linear partial differential equations†”, International Journal of Control, 14:2 (1971), 321  crossref
    7. J Mawhin, “Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces”, Journal of Differential Equations, 12:3 (1972), 610  crossref
    8. J.M Cushing, “Nonlinear Steklov problems on the unit circle. II (and a hydrodynamical application)”, Journal of Mathematical Analysis and Applications, 39:2 (1972), 267  crossref
    9. James P. Keener, Herbert B. Keller, “Perturbed bifurcation theory”, Arch Rational Mech Anal, 50:3 (1973), 159  crossref  mathscinet  zmath
    10. D. D. Joseph, “Repeated supercritical branching of solutions arising in the variational theory of turbulence”, Arch Rational Mech Anal, 53:2 (1974), 101  crossref  mathscinet  zmath  adsnasa
    11. David W. Zachmann, “Branching Solutions of Equations Containing Several Parameters”, SIAM J Math Anal, 5:6 (1974), 898  crossref  mathscinet
    12. Frank Hoppensteadt, “Analysis of Some Problems Having Matched Asymptotic Expansion Solutions”, SIAM Rev, 17:1 (1975), 123  crossref  mathscinet
    13. George H. Knightly, D. Sather, “Nonlinear Axisymmetric Buckled States of Shallow Spherical Caps”, SIAM J Math Anal, 6:6 (1975), 913  crossref  mathscinet  zmath
    14. J. B. McLeod, R. E. L. Turner, “Bifurcation for non-differentiable operators with an application to elasticity”, Arch Rational Mech Anal, 63:1 (1976), 1  crossref  mathscinet  zmath
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    24. Jamse P. Keener, “Infinite Period Bifurcation and Global Bifurcation Branches”, SIAM J Appl Math, 41:1 (1980), 127  crossref  mathscinet  isi
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    32. N. Damil, M. Potier-Ferry, “A New method to compute perturbed bifurcations: Application to the buckling of imperfect elastic structures”, International Journal of Engineering Science, 28:9 (1990), 943  crossref
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