Abstract
A usual linear Henstock–Kurzweil integral equation with respect to a simple discontinuous function may not have a solution. We propose to replace the value of the integral at the right endpoint of the integration domain by the left limit of its other values. We prove that the modified linear Henstock–Kurzweil integral equation with respect to a function h of bounded p-variation has a unique solution given by an extended Henstock–Kurzweil product integral of h over a right open interval.
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*This research was funded by a grant (No. MIP-053/2012) from the Research Council of Lithuania.
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Dirmeikis, Š., Norvaiša, R. An extended product integral, a modified linear integral equation, and functions of bounded p-variation*. Lith Math J 55, 343–366 (2015). https://doi.org/10.1007/s10986-015-9285-9
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DOI: https://doi.org/10.1007/s10986-015-9285-9