We establish the comparison theorem of integro--differential equations on infinite interval, and, by applying the lower-upper solution method, prove the existence of extreme solutions for nonlinear first order integro-differential equations on infinite interval in Banach spaces.

In this paper, the following initial value problem for nonlinear integro-differential equationu (t) =f(t, u(t),T1u(t), T,u(t) ) 1u(t)0=XO Iis considred, wbers \Using the method of upper and lower solutions and the monotone iteratiye technique, we obtain existence results of minimal and maximal solutions.

In this paper,we consider integro-differential equations kith 0<a<1,where p and q are constant.

Existence of the solution to singular boundary value problems for second order integro-differential equations;

Solutions of two-point boundary value problems of integro-differential equations in Banach spaces;

On monotone iterative method for the second order two point boundary value problems of integro-differential equations;

In this paper, we give the definition of locally Lipschitz continuous integrated C-semigroups and present a new method to solve an integro-differential equation by approximation of the convergence of integral of a sequence of C-semigroups.

By using the lower-upper solutions,the monotone iterative technique and a proper iterative process,the existence of global solutions of initial values for integral-differential equations in Banach spaces is obtained under weaker conditions.