Asymptotic Behavior of Certain Nonlinear Boundary‐Value Problems

The asymptotic properties of a class of nonlinear boundary‐value problems are studied. For large values of a parameter, the differential equation is of the singular‐perturbation type, and its solution is constructed by means of matched asymptotic expansions. In two special cases, very simple approximate analytic solutions are obtained, and their accuracy is illustrated by showing their good agreement with the exact numerical solution of the problem.