Geodesic
Quasilinear operators and Hammerstein's equation
Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 453-464.

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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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     author = {P. P. Zabreiko and A. I. Povolotskii},
     title = {Quasilinear operators and {Hammerstein's} equation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {453--464},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a12/}
}
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P. P. Zabreiko; A. I. Povolotskii. Quasilinear operators and Hammerstein's equation. Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 453-464. http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a12/