Implicit Vector Integral Equations Associated with Discontinuous Operators

Paolo Cubiotti and Jen-Chih Yao

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: Let I∶ = [0,1]. We consider the vector integral equation h(u(t)) = f(t, ∫Ig(t, z), u(z), dz) for a.e. t ∈ I, where f : I × J → R, g : I × I → [0, +∞[, and h : X → R are given functions and X, J are suitable subsets of Rn. We prove an existence result for solutions u ∈ Ls(I, Rn), where the continuity of f with respect to the second variable is not assumed. More precisely, f is assumed to be a.e. equal (with respect to second variable) to a function f* : I × J → R which is almost everywhere continuous, where the involved null‐measure sets should have a suitable geometry. It is easily seen that such a function f can be discontinuous at each point x ∈ J. Our result, based on a very recent selection theorem, extends a previous result, valid for scalar case n = 1.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2014/301675

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:301675

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().