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Title: Some explicit oscillation results for the generalised Liénard type systems

Authors: Tohid Kasbi; Vahid Roomi; Aliasghar Jodayree Akbarfam

Addresses: Faculty of Mathematics, University of Tabriz, Tabriz, 25529, Iran ' Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran ' Faculty of Mathematics, University of Tabriz, Tabriz, 25529, Iran

Abstract: In this work a generalised Liénard type system will be considered. We study the problem whether all trajectories of this system intersect the vertical isocline, which is very important in the global asymptotic stability of the origin, oscillation theory, and existence of periodic solutions. Under quite general assumptions we obtain sufficient conditions which are very sharp. We present some new conditions under which the solutions of this system are oscillatory. Some examples are provided to illustrate our results.

Keywords: oscillation; Liénard system; differential equations.

DOI: 10.1504/IJDSDE.2020.104899

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.1, pp.1 - 18

Received: 26 Jan 2018
Accepted: 03 May 2018

Published online: 05 Feb 2020 *

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