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 .
Citation
Paolo Cubiotti. Jen-Chih Yao. "Implicit Vector Integral Equations Associated with Discontinuous Operators." Abstr. Appl. Anal. 2014 1 - 6, 2014. https://doi.org/10.1155/2014/301675