【摘要】 研究含有慢变量的一类奇摄动非线性系统初始层现象,通过引进不同量级的伸长变量,构造不同"厚度"的初始层校正项,得到了摄动解关于小参数的N阶近似展开式,揭示了摄动解呈现的"层中层"现象,并利用不动点原理证明了摄动解的存在,给出了解的一致有效的渐近展开式·更多还原

【Abstract】 The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different "thickness", the N-order approximate expansion of perturbed solution concerning small parameter is obtained,and the "multiple layer" phenomena of perturbed solutions are revealed.Using the fixed point theorem,the existence of perturbed solution is proved, and the uniformly valid asymptotic expansion of the solutions is given as well.更多还原