Controllability criteria for semilinear measure driven evolution systems with impulses and nonlocal inclusions

This paper investigates the nonlocal controllability of semilinear measure driven evolution systems with impulsive effects and multivalued nonlocal inclusions in Banach spaces. The analysis is carried out in the Banach space of regulated functions, which naturally accommodates the discontinuities generated by impulsive phenomena and measure driven dynamics. By employing the Hausdorff measure of noncompactness together with a Mönch-type fixed point theorem, sufficient conditions for nonlocal controllability are established. The proposed approach avoids compactness assumptions on the evolution family that are typically required in classical controllability results for semilinear evolution systems. The obtained criteria describe the interaction among the evolution operator, the control operator, the measure driven nonlinear term, and the nonlocal inclusion. Finally, an impulsive partial differential equation is presented to illustrate the applicability of the theoretical results, and a finite-dimensional numerical example is provided to visualize the impulsive and measure driven dynamics.