On monotone iterative method for initial value problems of nonlinear second-order integro-differential equations in Banach spaces

Using the monotone iterative method and Mönch fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.