Article citationsMore>>

A. K. Zvonkin and M. A. Shubin, “Non-Standard Analysis and Singular Perturbations of Ordinary Differential Equations,” Russian Mathematical Surveys, Vol. 39, No. 2, 1984, pp. 69-131.
http://dx.doi.org/10.1070/RM1984v039n02ABEH003091

has been cited by the following article:

• TITLE: On the Two Methods for Finding 4-Dimensional Duck Solutions

  AUTHORS: Kiyoyuki Tchizawa

  KEYWORDS: Slow-Fast System; Singular Perturbation; Duck Solutions; Blowing-Up; Nonstandard Analysis

  JOURNAL NAME: Applied Mathematics, Vol.5 No.1, January 2, 2014

  ABSTRACT: This paper gives the existence of a duck solution in a slow-fast system in R2+2 using two ways. One is an indirect way and the other is a direct way. In the indirect way, the original system is once reduced to the slow-fast system in R2+1. In the direct one, it has a 4-dimensional duck solution when having an efficient local model. This is already published in [1,2]. Some sufficient conditions are given to get such a good model.