奇异摄动与鸭解

鸭解是近年来在奇异摄动方程的研究中发现并开始研究的，它是一种新的分支现象，关于这方面的结果不是很多，且在大多数文献中多采用非标准方法，本文则利和渐近分析法，微分方程定性理论及不动点方法，对一类特殊的单参数奇异摄动方程鸭解的存在性进行研究。给出了鸭解存在的充分条件及其所对应参数的估计；并给出了鸭解的近似表达式，利用这些结果可以清楚地描述这类方程当参数变化时相图的变化情况。

SINGULAR PERTURBATION AND DUCK SOLUTIONS

Duck solutions,a new kind of bifurcation phenomenon,are discovered and studied during the study of singular perturbation equations in the recent decades. Nonstandard method is used to research the duck solutions in most references and just limited results are obtained. This paper is mainly divoted to the study of existence of duck solutions of a special kind of one parameter singular perturbation equation by the asymptotic method,qualitative method of ordinary differential equations and fixed point method. We gave some sufficient conditions to guarantee the existence of duck solutions,the estimation of corresponding parameter and approximate expansion of duck solutions. So the phase portrait can be clearly depicted as the parameter changes.