Abstract
For a class of weakly non-linear oscillations involving a small parameter e we determine asymptotic solutions as ɛ ↓ 0 which are uniformly valid on some time interval. First, we consider a general initial-value problem in IR n containing a small parameter ɛ. We derive sufficient conditions for asymptotic correctness as ɛ ↓ 0 to be satisfied by formal asymptotic solutions. Next, we consider for the original problem formal asymptotic solutions of a two-variable type. For this type of formal asymptotic solutions the conditions for asymptotic correctness take a form which is very useful in the subsequent development of a construction technique for asymptotic solutions.
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