Asymptotic Solution for a Class of the Perturbation Equation with an Unbounded Interval

Using the matching asymptotic expansion method,this paper discussed a class of singular perturbed problems with unbounded interval.According to the changes of the parameter p in the problems,the paper divided the discussion about the equation into three cases and obtained the interior expansion of outer solution(yo)i and the outer expansion of interior solution(yi)o respectively.Using the matching principle of asymptotic expansion,the paper also got the general asymptotic solutions for this kind of problems,which can richen and expand the corresponding conclusions.