The singularly perturbation for there points boundary value problem of nonlinear third order equation is studied in this paper by means of differential inequality theories and the method of boundary layer correction.Under suitable assumptions,the author constructs specific upper and lower solutions,proves the existence of the solutions,and obtains the uniformly valid asymptotic expansion of the solutions.

By using the directly expanding method of the perturbation theory,the author discusses the equation ef(x)=g(x,e),where e is a positive small parameter.The asymptotic approximation of roots can be given according to the single root or multiple root of its reduced equation.