On the Polynomial Solutions and Limit Cycles of Some Generalized Polynomial Ordinary Differential Equations

Mathematics

Claudia Valls¹ 

[1] Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal;

关键词: polynomial ordinary differential equations;    polynomial solutions;   

DOI  :  10.3390/math8071139

来源: DOAJ

【 摘 要 】

We study equations of the form $ydy/dx=P(x,y)$ where $P(x,y)\in \mathbb{R}[x,y]$ with degree n in the y-variable. We prove that this ordinary differential equation has at most n polynomial solutions (not necessarily constant but coprime among each other) and this bound is sharp. We also consider polynomial limit cycles and their multiplicity.

【 授权许可】

Unknown