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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Carleman, T., Sur les équations intégrales singulières à noyau réel et symmétrique, Uppsala, 1923. Google Scholar

[2] 2. Costley, C. G., On singular normal integral equation, Canad. Math. Bull. (2) 13 (1970), 199-203. Google Scholar

[3] 3. Golomb, M., Zur Theorie der nicht linear en Integralgleichungen, Integralgleichungs System and allgemeinen Funktional-gleichungen, Math. Z. 39, 1934. Google Scholar

[4] 4. Hammerstein, A., Nichtlinear Integralgleichungen nebst Anwendungen, Acta Math. 54 (1930), 117-176. Google Scholar

[5] 5. Nemytsky, V., Théorèmes d'existance et d'unicite des solutions de quelques équations intégrales non-linéaires, Mat. Sb. 41, 1934. Google Scholar

[6] 6. Vainberg, M. M., Variational methods for the study of non-linear operators, Holden-Day, San Francisco, 1964. Google Scholar

[7] 7. Stone, M. H., Linear operators in Hilbert Space, Amer. Math. Soc., Colloq. Publication 1932. Google Scholar

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