On the Volterra integral equation in locally convex spaces. (English) Zbl 0781.45012

Bugajewski, Dariusz

Demonstr. Math. 25, No. 4, 747-754 (1992).

Let \(E\) be a sequentially complete locally convex topological vector space. The author considers integral equations of the form \((*)\) \(x(t)=g(t)+\int^ t_ 0f\bigl(t,s,x(s)\bigr)ds\). He gives a local existence theorem on some \(I:=[0,d]\) and proves that the set of all continuous solutions \(x:I\to E\) of \((*)\) is nonempty, compact and connected in \(C(I,E)\).

Reviewer: W.Petry (Düsseldorf)

MSC:

45N05	Abstract integral equations, integral equations in abstract spaces
45G10	Other nonlinear integral equations

Keywords:

Volterra integral equation; locally convex topological vector space; local existence theorem