Nonlinear Integral Equations of the Hammerstein Type(0 By
نویسنده
چکیده
fails to possess a solution in general if X is equal to any of the characteristic values X¡, ¿ = 1,2,3, , of the kernel __(x, y), it is not surprising that all treatments of (1) have been limited to the cases in which equation (2) is in some sense (to be made more precise later) a majorant for (1) when X =Xi, the smallest characteristic value of F"(x, y). Thus, if FT(x, y) is assumed to be positive-definite and symmetric, Hammerstein [1, Theorem l](2) proved that at least one solution would always exist when/(x, y) satisfied, for all y,
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