INVERSE PROBLEM FOR ABSTRACT DELAY DIFFERENTIAL EQUATION WITH IMPULSIVE EFFECTS

. In this manuscript, we consider an inverse problem (IP) for an abstract impulsive differential equation with constant delay. We identify the parameter using an over-determined condition on a mild solution. The main techniques to find the results are a direct approach using Volterra integral (VI) equations for sufficiently regular data and an optimal control approach for less regular data. In optimal control approach, the characterization of the limit of the sequence of approximate solutions demonstrates that it is a solution to the original IP, under certain hypotheses. Finally, we provide an example to showcase the precision and reliability of our findings.