Constructive existence and uniqueness for two-point boundary-value problems with a linear gradient term

摘要

Constructive existence and uniqueness theorems are established for nonlinear two-point boundary-value problems governed by the equation y″=f(x, y)+p(x)y′, 0⩽x⩽1. The existence and uniqueness is established for functions y(x) that satisfy a certain constraint, i.e., that sfncy(x)sfnc is bounded by a known function or that 0⩽y(x)⩽M for some M. Applications to scientific problems in the literature are given.