Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 71, pp. 1-8.

Title: Chiellini Hamiltonian Lienard differential systems

Authors: Jaume Gine (Univ. de Lleida, Lleida, Catalonia, Spain)
         Jaume Llibre (Univ. Autonoma de Barcelona, Catalonia, Spain)
         Claudia Valls (Instituto Superior Tecnico, Lisboa, Portugal)

Abstract:
 We characterize the centers of the Chiellini Hamiltonian Lienard
 second-order differential equations $x'=y$, $y'=-f(x) y -g(x)$ where
 $g(x)=f(x) (k - \alpha (1 +\alpha) \int f(x) dx )$ with
 $\alpha, k \in \mathbb{R}$. Moreover we study the phase portraits
 in the Poincare disk of these systems when $f(x)$ is linear.

Submitted January 26, 2019. Published May 17, 2019.
Math Subject Classifications: 34C05, 34A34, 34C14.
Key Words: Lienard system; center-focus problem; first integrals.