Existence results for systems of abstract evolution equations with nonlocal initial conditions

This paper investigates the existence of solutions for systems of abstract evolution equations subject to nonlocal initial conditions. Our approach is based on a combination of the fixed point theorems due to Perov, Schauder and Avramescu, together with the semigroup method and a matrix-based technique involving vector-valued norms. The results presented here generalize and refine existing theorems in the literature.