Abstract
© 2016 Royal Society of Edinburgh. We study the existence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x' = y, y' =-g(x)-f(x)y, where f(x) = 3Q(x)Q'(x)P(x) + Q(x)2 P'(x) and g(x) = Q(x)Q'(x)(Q(x)2 P(x)2-1) with P,Q [x]. This class of generalized Liénard polynomial differential systems has the invariant algebraic curve (y + Q(x)P(x))2-Q(x)2 = 0 of hyperelliptic type.
| Original language | English |
|---|---|
| Pages (from-to) | 1195-1210 |
| Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
| Volume | 146 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 1 Dec 2016 |
Keywords
- Darboux polynomial
- Liouvillian first integral
- Liénard polynomial differential system
- exponential factor
- invariant algebraic curve