Electron. J. Diff. Equ., Vol. 2013 (2013), No. 23, pp. 1-19.

Darboux integrability and rational reversibility in cubic systems with two invariant straight lines

Dumitru Cozma

We find conditions for a singular point O(0,0) of a center or a focus type to be a center, in a cubic differential system with two distinct invariant straight lines. The presence of a center at O(0,0) is proved by using the method of Darboux integrability and the rational reversibility.

Submitted December 1, 2011. Published January 27, 2013.
Math Subject Classifications: 34C05.
Key Words: Cubic differential systems; center problem; invariant straight lines; Darboux integrability; rational reversibility.

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Dumitru Cozma
Tiraspol State University
5 Gh. Iablocichin str.
Chisinau, MD-2069, Moldova
email: dcozma@gmail.com

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