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Mat. Zametki, 1972, Volume 12, Issue 4, Pages 453–464 (Mi mz9904)  

Quasilinear operators and Hammerstein's equation

P. P. Zabreikoa, A. I. Povolotskiib

a Yaroslav State University
b Leningrad State Pedagogical Institute

Abstract: We describe the class of operators in a Hilbert space $\mathrm{H}$, introduced by A. I. Perov, which can be represented in the form $\mathrm{Ax=D(x)x}$, where $\mathrm{D(x)}$ is a self-conjugate operator satisfying the inequalities $\mathrm{B_-\leqslant D(x)\leqslant B_+}$ ($\mathrm{B_-}$ and $\mathrm{B_+}$ are fixed self-conjugate operators). As an application we obtain new theorems on the solvability of Hammerstein's equation.

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English version:
Mathematical Notes, 1972, 12:4, 705–711

Bibliographic databases:

UDC: 517.4
Received: 07.04.1971

Citation: P. P. Zabreiko, A. I. Povolotskii, “Quasilinear operators and Hammerstein's equation”, Mat. Zametki, 12:4 (1972), 453–464; Math. Notes, 12:4 (1972), 705–711

Citation in format AMSBIB
\Bibitem{ZabPov72}
\by P.~P.~Zabreiko, A.~I.~Povolotskii
\paper Quasilinear operators and Hammerstein's equation
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 4
\pages 453--464
\mathnet{http://mi.mathnet.ru/mz9904}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=326523}
\zmath{https://zbmath.org/?q=an:0246.47067}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 4
\pages 705--711
\crossref{https://doi.org/10.1007/BF01093678}


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