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Abstract and Applied Analysis
Volume 2015, Article ID 456364, 8 pages
http://dx.doi.org/10.1155/2015/456364
Research Article

On the Equivalence of Differential Equations in the Sense of Coincidence Reflecting Functions

School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China

Received 7 March 2015; Revised 17 April 2015; Accepted 20 April 2015

Academic Editor: Jaume Giné

Copyright © 2015 Zhengxin Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We use a new method for constructing some differential equations which are equivalent to a given equation in the sense of having the same reflecting function. We completely solve the problem: when is a polynomial differential equation equivalent to a given polynomial differential equation? Many sufficient conditions have been established for one differential equation to be equivalent to a given differential equation. We apply the obtained results to study the boundary value problem of two equivalent differential equations.