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Mat. Sb. (N.S.), 1972, Volume 87(129), Number 3, Pages 324–337 (Mi msb3127)  

This article is cited in 3 scientific papers (total in 3 papers)

Nonlinear equations of Hammerstein type with potential and monotone operators in Banach spaces

M. M. Vainberg, I. M. Lavrent'ev


Abstract: We prove an existence and uniqueness theorem for solutions of equations of Hammerstein type
\begin{equation} x=SF(x) \end{equation}
in Banach spaces. The main difference between this study and previous ones is to be found in the assumptions that $S$ is a closed operator from one Banach space into another, and that bounds on $F$ are imposed only on certain subsets of the space in question. The proof of the basic results requires an extension of the nonlinear mappings; we do not assume continuity of these mappings. The concept of a generalized solution is introduced, and sufficient conditions are found for it to be unique, and to coincide with an exact solution.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1972, 16:3, 333–347

Bibliographic databases:

UDC: 517.934
MSC: Primary 47H99; Secondary 47H05
Received: 04.12.1970

Citation: M. M. Vainberg, I. M. Lavrent'ev, “Nonlinear equations of Hammerstein type with potential and monotone operators in Banach spaces”, Mat. Sb. (N.S.), 87(129):3 (1972), 324–337; Math. USSR-Sb., 16:3 (1972), 333–347

Citation in format AMSBIB
\Bibitem{VaiLav72}
\by M.~M.~Vainberg, I.~M.~Lavrent'ev
\paper Nonlinear equations of Hammerstein type with potential and monotone operators in Banach spaces
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 87(129)
\issue 3
\pages 324--337
\mathnet{http://mi.mathnet.ru/msb3127}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=296776}
\zmath{https://zbmath.org/?q=an:0249.47062}
\transl
\jour Math. USSR-Sb.
\yr 1972
\vol 16
\issue 3
\pages 333--347
\crossref{https://doi.org/10.1070/SM1972v016n03ABEH001429}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R Kannan, John Locker, “Operators and nonlinear Hammerstein equations”, Journal of Mathematical Analysis and Applications, 53:1 (1976), 1  crossref
    2. R KANNAN, J LOCKER, “Nonlinear boundary value problems and operators”, Journal of Differential Equations, 28:1 (1978), 60  crossref
    3. Durante T. Kupenko O.P. Manzo R., “on Attainability of Optimal Controls in Coefficients For System of Hammerstein Type With Anisotropic P-Laplacian”, Ric. Mat., 66:2 (2017), 259–292  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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