| Abstract: | A study is made of a two-point nonlinear boundary-value problem with a small parameter multiplying the highest derivative. It is shown that under certain circumstances the asymptotic solution to the problem is expressible in terms of the solution to a linear boundary-value problem—in which case the two problems are said to be asymptotically equivalent. The coefficients of the linear problem necessarily satisfy certain conditions, and these conditions are shown to bear a close relationship to the equations obtained in constructing a solution to the nonlinear problem by standard matching methods. |
