Existence and stability results for a class of nonlocal semilinear equations involving delays

We investigate the existence and weak stability of mild solutions for a class of nonlocal semilinear equations involving finite delays. Based on local estimates and fixed point arguments, we prove the global existence of mild solutions to problems in which the nonlinearity is superlinear or sublinear without the smallness condition on initial data or on the coefficients. Then by using a special measure of noncompactness, we show some sufficient conditions ensuring the weak stability of mild solutions.