On existence of nonlinear measure driven equations involving non-absolutely convergent integrals

In this paper, we study the existence of solutions for nonlinear measure driven equations in Kurzweil integral setting. Firstly, some new results on Hausdorff measure of noncompactness in the space of regulated functions are established. Then some existence criteria of the measure system are provided by applying Hausdorff measure of noncompactness and a corresponding fixed point theorem. The results in this paper improve and generalize those well known in the literature. Finally, an example is given to illustrate our results.