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

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
$$x=SF(x)$$
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

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
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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
2. R KANNAN, J LOCKER, “Nonlinear boundary value problems and operators”, Journal of Differential Equations, 28:1 (1978), 60
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
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