On the existence of at least one solution for functional integral equations via the measure of noncompactness
- Authors: Vetro, C; Vetro, F
- Publication year: 2017
- Type: Articolo in rivista (Articolo in rivista)
- OA Link: http://hdl.handle.net/10447/241663
Abstract
In this article, we use fixed-point methods and measure of noncompactness theory to focus on the problem of establishing the existence of at least a solution for the following functional integral equation $$u(t) = g (t, u(t)) + \int_0^t G(t, s, u(s))ds,\quad t \in [0,+\infty[,$$ in the space of all bounded and continuous real functions on $\mathbb{R}_+$, under suitable assumptions on $g$ and $G$. Also, we establish an extension of Darbo's fixed-point theorem and discuss some consequences.