【摘要】 针对非线性常微分方程定解问题以及非线性常微分方程奇异摄动初值问题的诸多研究,指出一类三阶非线性奇摄动初值问题存在套层解.通过理论分析证实解的边界层项的指数性质,使用微分不等式和比较定理,揭示了问题解的套层现象,证明了解的一致有效性.研究结果表明:对解决其他三阶问题和高阶问题有借鉴和推广意义.更多还原

【Abstract】 There are many problems need to be solved in the study of well posed solution to an ordinary differential equation problem.The investigation of the initial singular perturbation value for nonlinear ordinary differential equation initial problem is in developing stage.This paper indicated that the cover layer phenomenon exists in the singularly perturbed initial problem of the class of third order nonlinear ordinary differential equation.On the basis of author’s original work and by means of differential inequalities and comparison theorem,this paper verified properties for the solution of boundary layer term and revealed the existing of cover layer in solution of the problem.Finally,the uniform validity of asymptotic solution is proved.The result of study has reference and popularization value for solution to other problems of third order and higher order.更多还原