论文标题
在Poizat和Liénard的方程式上
On the equations of Poizat and Liénard
论文作者
论文摘要
我们研究了第二个阶差分方程（Poizat方程）的通用差分方程中的溶液集的结构，这些方程是liénard方程的特定情况。我们为该类别的方程式提供了必要和充分的条件，并为强度最小的Poizat方程解决方案的代数关系提供了完整的分类。我们还对非强度最小的案例以及有关某些Liénard方程的Liouvillian和Pfaffian解决方案的应用进行了分析。
We study the structure of the solution sets in universal differential fields of certain differential equations of order two, the Poizat equations, which are particular cases of Liénard equations. We give a necessary and sufficient condition for strong minimality for equations in this class and a complete classification of the algebraic relations for solutions of strongly minimal Poizat equations. We also give an analysis of the non strongly minimal cases as well as applications concerning the Liouvillian and Pfaffian solutions of some Liénard equations.
