Geodesic
On a Solution of the Hammerstein Equation with Singular Normal Kernels
Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 415-421

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We consider here the equation 1 This equation was first studied by Hammerstein [4] under the assumption that the linear operator 2 is selfadjoint and completely continuous. V. Nemytsky [5] and M. Golomb [3] dropped the assumption that A be selfadjoint and positive. M. Vainberg [6] considered (among other cases) the case in which A is a bounded operator generated by a Carleman kernel. The kernels considered in this work do not necessarily generate bounded, completely continuous or selfadjoint, operators. 
Costley, Charles G. On a Solution of the Hammerstein Equation with Singular Normal Kernels. Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 415-421. doi: 10.4153/CMB-1970-077-7
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     author = {Costley, Charles G.},
     title = {On a {Solution} of the {Hammerstein} {Equation} with {Singular} {Normal} {Kernels}},
     journal = {Canadian mathematical bulletin},
     pages = {415--421},
     year = {1970},
     volume = {13},
     number = {4},
     doi = {10.4153/CMB-1970-077-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-077-7/}
}
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