Results on inverse problem for abstract semilinear differential inclusions

Abstract In this manuscript, we examine an inverse problem for abstract semilinear differential inclusions. We identify the unknown parameter using the given overdetermined condition. We establish the existence of mild solution to the considered inverse problem. Further, the continuous dependence of the solution to the initial data is discussed.The main tools to obtain the results are Banach fixed point theorem, Grönwall’s inequality, set-valued theory and semigroup theory. Moreover, we provide several examples and some graphical illustrations to validate our findings.