A NOTE ON UPPER AND LOWER SOLUTIONS METHOD FOR FOURTH-ORDER BOUNDARY VALUE PROBLEMS

In this paper,we deal with a class of boundary value problem.We give the existence of solution under the assumption that there exist lower and upper solutions to the problem.Our result extends and complements the relevant ones which were obtained by many authors previously.

EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS

This paper is concerned with the following second-order vector boundary value problem ：x^R=f（t,Sx,x,x＇）,0〈t〈1,x（0）=A,g（x（1）,x＇（1））=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method.

Existence and Uniqueness of Positive Solutions for Some Singular Boundary Value Problems with Linear Functional Boundary Conditions

By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f（t, u） is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0, 1] positive solutions as well as the C1 [0, 1] positive solutions.

ASYMPTOTIC BEHMIOUR IN A REACTION-DIFFUSION SYSTEM

This paper proves the asymptotic behaviour for a class of reaction-diffusionsystem in bacteriology by using duality technique, semigroup theorem, Lp--estimates andupper and lower solutions method.

BOUNDARY VALUE PROBLEM FOR NON-LINEAR SECOND ORDER ORDINARY DIFFERENTIAL EQUATION WITH DISCONTINUOUS TERMS IN BANACH SPACE

By using upper and lower solutions and fixed point theorem we give the existence theorem of non-linear second order ordinary differential equation with discontinuous terms in Banach Space.

A Class of Singularly Perturbed Boundary Value Problems Arising from Catalytic Reactions

A class of singularly perturbed boundary value problems arising from the catalytic reactions in chemical engineering is observed. That kind of p roblems exhibits the behavior of nonexponentially decayed boundary layer, and he nce the study of asymptotic behavior of their solutions seems more diffcult. The uniformly valid asymptotic expansions of solutions as well as their derivatives are given via the upper and lower solutions method, and those estimates seem qu ite accurate.

A NUMERICAL METHOD FOR SOLVING NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF FREDHOLM TYPE

The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterative method yields two sequences which converge monotonically from above and below, respectively, to a solution of a nonlinear difference scheme. This monotone convergence leads to an existence-uniqueness theorem. An analy- sis of convergence rates of the monotone iterative method is given. Some basic techniques for construction of initial upper and lower solutions are given, and numerical experiments with two test problems are presented.

BOUNDARY VALUE PROBLEM FOR FIRST ORDER IMPULSIVE DIFFERENTIAL EQUATION WITH A PARAMETER AND INFINITE DELAY

In this paper, we consider a boundary problem of first order impulsive differential equation with a parameter and infinite delay. By using the method of upper and lower solutions, we get some sufficient conditions for the existence of its solutions.