奇摄动非线性微分方程初值问题的双重层解

本文研究一类二阶非线性微分方程初值问题的奇摄动，揭示了其解呈现双重层性质，在适当的假设条件下，利用微分不等式理论，得到了解的存在性和具有不同量级校正项的渐近开式。

DOUBLE LAYER BEHAVIOR IN SINGULAR PERTURBED NONLINEAR DIFFERENTIAL EQUATIONS FOR INITIAL VALUE PROBLEM

In this paper, we study the singular perturbation of initial value problem for a class of second order nonlinear differential equation, the solution is shown to exhibit double layer behavior. Under appropriate conditions, using the theory of differential inequality, the author gets the existence of the solution and its asymptotic estimation with correction terms for different order of magnitude.