In this paper, the split fixed point and variational inclusion problem is considered. With help of technique, Tseng-type splitting method self-adaptive rule, an iterative algorithm proposed for solving in which involved operators S T are demicontractive g plain monotone. Strong convergence theorem proved under some mild conditions.

In this paper, we consider the existence of extremal solutions for nonlinear fourth-order differential equation. By use a new comparison result, some sufficient conditions are established by combining monotone iterative technique and methods lower upper solutions. Finally, an example is given to illustrate validity our main results.

In this paper, we solve numerically a semiconductor device energy balance equation using monotone iterative method. With the proposed solution technique, we prove the solution of ̄nite volume discretized semiconductor device energy balance equation converges monotonically. The method presented here provides an e± cient approach for the numerical solution of energy balance equation in submicron ...

This paper is concerned with the existence of extreme solutions of the three-point boundary value problem for a class of second order functional differential equations. We introduce new concept of lower and upper solutions. By using the method of upper and lower solutions and monotone iterative technique, we obtain the existence of extreme solutions.

The monotone iterative technique, theory of fixed point index in a cone and the Leggett-Williams theorem are applied to investigate existence multiplicity positive solutions for four boundary value problems nonlinear fractional differential equations with p-Laplacian operator infinite delay. Moreover, examples presented illustrate vast applicability our main results.

This paper is concerned with the nonlinear boundary value problems for first order integro-differential equations with impulsive integral conditions. By using of the method of lower and upper solutions coupled with the monotone iterative technique, we give conditions for the existence of extremal solutions.

Abstract In the paper, nonlinear systems of mixed-type functional differential equations are analyzed and existence semi-global global solutions is proved. proofs, monotone iterative technique Schauder-Tychonov fixed-point theorem used. addition to proving solutions, estimates their co-ordinates derived as well. Linear variants results considered illustrated by selected examples.

This paper deals with the existence of L-quasi-solutions for impulsive periodic boundary value problems in an ordered Banach space E. Under a new concept of upper and lower solutions, a new monotone iterative technique on periodic boundary value problems of impulsive differential equations has been established. Our result improves and extends some relevant results in abstract differential equat...

In this paper, the method of upper and lower solutions and monotone iterative technique are employed to the study of nonlinear three-point boundary value problems for a class of first order impulsive integro-differential equations of mixed type. Sufficient conditions for the existence of extreme solutions are obtained. Mathematics Subject Classification: 34B37