×

zbMATH — the first resource for mathematics

On Volterra integral equations with weakly singular kernels in Banach spaces. (English) Zbl 0791.45006
The author considers the integral equation \(x(t)=g(t)+\int_{D(t)} A(t,s) f(s,x (s)) ds\), \(t \in\mathbb{R}^ n\), \(D(t)=\{s \in \mathbb{R}^ n | 0 \leq s_ i \leq t_ i\}\), where \(A\) is weakly singular and \(x\) takes values in a Banach space \(E\). Under certain additional conditions it is shown that there exists \(J=[0,j_ 1] \times\cdots \times [0,j_ n]\) such that the set of all continuous solutions \(x:J \to E\), considered as a subset of \(C(J,E)\), is a compact \(R_ \delta\).

MSC:
45N05 Abstract integral equations, integral equations in abstract spaces
45G05 Singular nonlinear integral equations
PDF BibTeX XML Cite
Full Text: DOI