An extension of Dragilev's theorem for the existence of periodic solutions of the Liénard equation
Subject of this paper is the well-known and intensively studied Liénard equation. The authors discuss the conditions and methods for guaranteeing the existence of at least one (nontrivial) periodic orbit (referring partly to former papers by one of the present authors). Since the classical Poincaré-Bendixson theorem seems to be the only available device to do this, it is important to construct a so-called winding trajectory by applying either of two methods: the energy method and the method of intersection with the vertical isocline. In this way, the authors derive an improvement of a theorem by \textit{A. V. Dragilev} [Prikl. Mat. Mekh. 16, 85--88 (1952; Zbl 0046.09703)] on the existence of a limit cycle. Finally, they indicate how the conditions may be adjusted in such a way that there exist at least two limit cycles.
scientific article; zbMATH DE number 6487753
scientific article