Implicit Vector Integral Equations Associated with Discontinuous Operators

Paolo Cubiotti and Jen-Chih Yao

Abstract and Applied Analysis, 2014, vol. 2014, 1-6

Abstract:

Let . We consider the vector integral equation for a.e. where and are given functions and are suitable subsets of . We prove an existence result for solutions , where the continuity of with respect to the second variable is not assumed. More precisely, is assumed to be a.e. equal (with respect to second variable) to a function which is almost everywhere continuous, where the involved null-measure sets should have a suitable geometry. It is easily seen that such a function can be discontinuous at each point . Our result, based on a very recent selection theorem, extends a previous result, valid for scalar case .

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:301675

DOI: 10.1155/2014/301675

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