Solutions and positive solutions for some three-point boundary value problems (Q1422516)

By applying a Gronwall inequality, the author studies the existence of a solution for some second-order three-point boundary value problems, where the nonlinearity is allowed to have nonlinear growth. Then, he shows the existence of at least one positive solution for a second-order three-point boundary value problem, where the nonlinearity involves the first derivative by using a fixed-point theorem in cone.