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Zbl 0625.45013
Banaś, Józef
An existence theorem for nonlinear Volterra integral equation with deviating argument.
(English)
[J] Rend. Circ. Mat. Palermo, II. Ser. 35, 82-89 (1986). ISSN 0009-725X; ISSN 1973-4409/e

The paper deals with nonlinear Volterra integral equations with deviating argument $$x(t)=h(t)+\int\sp{t}\sb{0}K(t,s,x(H(s)))ds,\quad t\ge 0,$$ in $C\sb g$ spaces: $C\sb g(R\sb+,R\sp n)=\{x: R\sb 0\to R\sp n$, continuous and $\vert x(t)\vert /g(t)$ bounded on $R\sb+\}$. It is assumed that g is a continuous positive function on $R\sb+$. Under various conditions on the data it is shown that the equation under discussion has at least one solution in a convenient $C\sb g$ space (using Schauder fixed point theorem). The classical case of Volterra equation is covered by the result.
[C.Corduaneanu]
MSC 2000:
*45G10 Nonsingular nonlinear integral equations
45D05 Volterra integral equations

Keywords: existence; nonlinear Volterra integral equations with deviating argument; Schauder fixed point theorem

Cited in: Zbl 1038.45005 Zbl 0715.45001

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