  This work is concerned with the existence and uniqueness of boundary value
problems defined on semi-infinite intervals. These kinds of problems seldom
admit exactly known solutions and, therefore, the theoretical information on
their well-posedness is essential before attempting to derive an approximate
solution by analytical or numerical means. Our utmost contribution in this
context is the definition of a numerical test for investigating the existence
and uniqueness of solutions of boundary problems defined on semi-infinite
intervals. The main result is given by a theorem relating the existence and
uniqueness question to the number of real zeros of a function implicitly
defined within the formulation of the iterative transformation method. As a
consequence, we can investigate the existence and uniqueness of solutions by
studying the behaviour of that function. Within such a context the numerical
test is illustrated by two examples where we find meaningful numerical results.
