WELL-POSEDNESS OF NONLOCAL IMPULSIVE PROBLEMS OF NON-AUTONOMOUS EVOLUTION EQUATIONS WITH DELAY

This paper investigates the existence of extremal mild solutions for nonlocal impulsive problems of non-autonomous evolution equations with delay in ordered Banach spaces. By applying the perturbation technique and monotone iterative method in the presence of lower and upper solutions, we establish the existence of the minimal and maximal mild solutions under suitable monotonicity conditions and noncompactness measure requirements of nonlinear term. Furthermore, we prove the existence of at least one mild solution and obtain the uniqueness of mild solution between the lower and the upper solutions.