The existence result of extreme solutions for periodic boundary value problem for second order impulsive functional differential equation is discussed by using the method of lower and upper solutions coupled with monotone iterative technique.

In this paper,by using the monotone iterative technique,the unique solution for nonlinear mixed monotone impulsive Volterra integral equations in Banach spaces is investigated under the more extensive conditions.

Using the lower and upper solutions method monotone iterative techniques,the existence of maximal and minimal solutions of first order implusive integro differential equations of mixed type are obtained.

By employing the approaches for upper and lower solutions and monotone iterative technique,the authors have obtained the sufficient conditions for the existence of coupled maximal solution and minimal solution.

Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results.

We obtain the existence of extremal solutions of the boundary value problem by using the method of lower and upper solutions coupled with monotone iterative technique.

First,we constructed a pair of appropriate upper and lower solutions,and then we proved the existence of the traveling wave solutions between two equilibria of the system by using the monotone iteration approach.

This paper is devoted to investigate a kind of lattice Nicholson s blowflies model with delay,and prove the existence of traveling wavefronts by upper-lower solution and monotone iteration technique.

It is shown that the system exist monotone traveling wave solutions by using monotone iteration with upper and lower solutions provided wave speed satisfies some conditions.

The method of upper and lower solutions and the monotone iterative technique are used.

By using cone theorem and monotone iterative method, the mixed monotone condition in A(x,y)+Mx in Banach spaces is extended.

It obtains the existence results by using the monotone iterative method of lower and upper solutions and improves the results.

In this paper,the monotone iterative technique for periodic boundary value problems with causal operators is developed.

The existence of solutions and coupled minimal and maximal quasi-solutions of nonlinear Volterra impulsive integral equations in ordered Banach spaces is given by monotone iterative technique under G(t,s,x) and I_k(k=1,2,…,m) without monotone conditions.

Under the compact type condition,a comparision theorem and monotone iterative techniques are founded on ,+∞) by using the theory of noncompactness measure and upper and lower solutions method,three existence results of global solutions are obtained for a initial value problem of ordinary differential equation in Banach spaces.

The existence and uniqueness of solution and maximum principle about linear first order integrodifferential equation are given,then,using it,the monotone iterative method for PBVP of first order integrodifferential equations is discussed.

The existence of solutions for multi-point boundary value problem with p-Laplacian operator is investigated by using monotone iterative method.

A new maximum principle and monotone iterative method of lower and upper solutions are employed to establish existence result for the third-order boundary value problem-u″′(t)=f(t,u(t)),t∈,u(0)=u\'(0)=u(1)=0.