Iterative Solution for Systems of Binary Non-mixed Monotone Operator Equations

With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATIONS

The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].

Fixed Point Theorems of Mixed Monotone Operators with Applications

In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.

Existence and Uniqueness of Fixed Points for Mixed Monotone Operators with Application

In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.

Mixed Monotone Iterative Technique and Boundary Value Problem for a Class of Impulsive Integro-Differential Equations

In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.

EXISTENCE OF SOLUTIONS FOR MIXED MONOTONE IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES

This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mixed monotone iterative technique and Monch fixed point theorem, Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. Finally, an example is worked out.

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR SINGULAR 2mth-ORDER CONTINUOUS AND DISCRETE LIDSTONE BOUNDARY VALUE PROBLEMS

By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR INITIAL VALUE PROBLEMS OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

In this paper, the initial value problems of second order ordinary differential equations in Banach spaces are discussed. By using the monotone iterative technique, some existence and uniqueness theorems for solutions are obtained.

The Existence of Coupled Solutions for a Kind of Nonlinear Operator Equations in Partial Ordered Linear Topology Space

The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method. Some new existence results are obtained.

Existence and Uniqueness of Solutions to Singular Higher Order Two-point BVPs on Time Scales

This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method.The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem.

MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES

This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.

The Existence of Positive Almost Periodic Type Solutions for Some Nonlinear Delay Integral Equations

This paper presents the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations, by using a fixed point theorem in the mixed monotone operators （Ma, Y.： On a class of mixed monotone operators and a kind of two-point bounded value problem. Indian J. Math., 41（2）, 211-220 （1999]]. Some known results are operators.

EXISTENCE OF POSITIVE SOLUTION TO TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.