In this paper, we present the Green’s functions for a second-order linear differential equation with three-point boundary conditions. We give exact expressions of the solutions for the linear three-point boundary problems by the Green’s functions. As applications, we study uniqueness and iteration of the solutions for a nonlinear singular second-order three-point boundary value problem.

We consider nonlinear boundary value problems with multiple solutions. A method is proposed for the computation of such solutions which depends crucially on known a priori qualitative information about the behavior of the solutions. The method is a two-stage method where the second stage is a shooting method and initial values of the shooting parameters are found in a first stage which approxim...

This paper studies the boundary value problems for the fourth-order nonlinear singular difference equationsΔ4u i−2 λα i f i, u i , i ∈ 2, T 2 , u 0 u 1 0, u T 3 u T 4 0. We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems i...

Some existence theorems of the positive solutions and the multiple positive solutions for singular and nonsingular systems of nonlinear fourth-order boundary value problems are proved by using topological degree theory and cone theory.

where φp(s) is a p-Laplacian operator, that is, φp(s)= |s|p−2s, p > 1, η ∈ (0,1) is a given constant, α > 0, γ > 0, β ≥ 0, δ ≥ 0, g : [0,1]→ [0,∞) has countable many singularities on (0,1/2). In recent years, because of the wide mathematical and physical backgrounds [7, 8], the existence of positive solutions for nonlinear boundary value problems with p-Laplacian received wide attention. Especi...