Abstract
Consider a system of nonlinear integral equations of Volterra-type (P) x(t) f(t)+[o g(t, s, x(s))ds. Recently R. K. Miller and G. R. Sell [1] proved some fundamental theorems of (P) under airly general assumptions on f(t) and g(t, s, x) similaro the Carathodory-ype. They showed that the cross-section F(t)=(y’y=x(t), where x is some solution of (P)} is compact in R for all t e [0, a), where a is either c or a finite number such that there is a solution x(t) of (P)or which limsup. x(t) c. This appears to be a generalization of H. Kneser’s theorem to integral equations.
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