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
We prove an existence and uniqueness theorem for solutions of equations of Hammerstein type
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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Mathematics of the USSR-Sbornik, 1972, 16:3, 333–347
MSC: Primary 47H99; Secondary 47H05
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
\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.)
\jour Math. USSR-Sb.
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This publication is cited in the following articles:
R Kannan, John Locker, “Operators and nonlinear Hammerstein equations”, Journal of Mathematical Analysis and Applications, 53:1 (1976), 1
R KANNAN, J LOCKER, “Nonlinear boundary value problems and operators”, Journal of Differential Equations, 28:1 (1978), 60
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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