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LIMIT CYCLES IN DISCONTINUOUS GENERALIZED LIÉNARD DIFFERENTIAL EQUATIONS
  • Zouhair Diab
Zouhair Diab
University of Tebessa
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Peer review status:UNDER REVIEW

04 Jul 2020Submitted to Mathematical Methods in the Applied Sciences
10 Jul 2020Assigned to Editor
10 Jul 2020Submission Checks Completed
21 Jul 2020Reviewer(s) Assigned

Abstract

The goal of this paper is to study the number of limit cycles that can bifurcate from the periodic orbits of a linear center perturbed by nonlinear functions inside the class of all generalized Liénard di¤erential equations allowing discontinuities. In particular our results show that for any n 1 there are di¤erential equations of the form x¨+f(x; x_ )x_ +x+sgn(x_ )g(x) = 0, with f and g polynomials of degree n and 1 respectively, having [n=2] + 1 limit cycles, where [] denotes the integer part function.