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Villari, G. and Zanolin, F. (1990) On a Dynamical System in the Liénard Plane. Necessary and Sufficient Conditions for the Intersection with the Vertical Isocline and Applications. Funkcialaj Ekvacioj, 33, 19-38.

has been cited by the following article:

• TITLE: Necessary and Sufficient Conditions for Oscillations of the Generalized Liénard Systems

  AUTHORS: Hongtao Zhang, Xiaolin Liu, Ping Yan

  KEYWORDS: Generalized Liénard System, Nonlinear Integral Inequality, Oscillation

  JOURNAL NAME: Applied Mathematics, Vol.15 No.6, June 26, 2024

  ABSTRACT: In this paper, we study the second-order nonlinear differential systems of Liénard-type x ˙ = 1 a( x ) [ h( y )−F( x ) ] , y ˙ =−a( x )g( x ) . Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.