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An existence theorem for nonlinear Volterra integral equation with deviating argument. (English) Zbl 0625.45013

The paper deals with nonlinear Volterra integral equations with deviating argument

x(t)=h(t)+ 0 t K(t,s,x(H(s)))ds,t0,

in C g spaces: C g (R + ,R n )={x:R 0 R n , continuous and |x(t)|/g(t) bounded on R + }. It is assumed that g is a continuous positive function on R + . Under various conditions on the data it is shown that the equation under discussion has at least one solution in a convenient C g space (using Schauder fixed point theorem). The classical case of Volterra equation is covered by the result.

Reviewer: C.Corduaneanu

45G10Nonsingular nonlinear integral equations
45D05Volterra integral equations
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