Open Access
2014 Implicit Vector Integral Equations Associated with Discontinuous Operators
Paolo Cubiotti, Jen-Chih Yao
Abstr. Appl. Anal. 2014: 1-6 (2014). DOI: 10.1155/2014/301675


Let I=[0,1]. We consider the vector integral equation h(u(t))=ft,Ig(t,z),u(z),dz for a.e. tI, where f:I×JR,g:I×I [0,+[, and h:XR are given functions and X,J are suitable subsets of Rn. We prove an existence result for solutions uLs(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×JR 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 xJ. Our result, based on a very recent selection theorem, extends a previous result, valid for scalar case n=1.


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Paolo Cubiotti. Jen-Chih Yao. "Implicit Vector Integral Equations Associated with Discontinuous Operators." Abstr. Appl. Anal. 2014 1 - 6, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022116
MathSciNet: MR3198172
Digital Object Identifier: 10.1155/2014/301675

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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