Abstract: We study the existence of positive solutions to the three
points difference-summation boundary value problem. We show the
existence of at least one positive solution if f is either superlinear or
sublinear by applying the fixed point theorem due to Krasnoselskii
in cones.
Abstract: In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.