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On the center of the generalized Liénard system

Cheng Dong Zhao, Qi-Min He (2002)

Czechoslovak Mathematical Journal

In this paper, we discuss the conditions for a center for the generalized Liénard system d x d t = ϕ ( y ) - F ( x ) , d y d t = - g ( x ) , or d x d t = ψ ( y ) , dy d t = - f ( x ) h ( y ) - g ( x ) , with f ( x ) , g ( x ) , ϕ ( y ) , ψ ( y ) , h ( y ) , F ( x ) = 0 x f ( x ) d x , and x g ( x ) > 0 for x 0 . By using a different technique, that is, by introducing auxiliary systems and using the differential inquality theorem, we are able to generalize and improve some results in [1], [2].

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