Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 41, pp. 1-36.

Title: Crossing limit cycles for a class of  piecewise linear
       differential centers separated by a conic
       
Authors: Johana Jimenez (Univ. Federal do Oeste da Bahia, Brazil)
         Jaume Llibre (Univ. Autonoma de Barcelona, Catalonia, Spain)
         Joao C. Medrado (Univ., Federal de Goias, Brazil)

Abstract:
 In previous years the study of the version of Hilbert's 16th problem
 for  piecewise linear differential systems in the plane has
 increased. There are many papers studying the maximum
 number of crossing limit cycles when the differential system is
 defined in two zones separated by a straight line. 
 In particular in [11,13]  it was proved that piecewise
 linear differential centers separated by a straight line have no
 crossing limit cycles. However in [14,15] 
 it was shown that the  maximum number of crossing
 limit cycles of piecewise linear differential centers can change
 depending of the shape of the discontinuity curve. In this work
 we study the maximum number of crossing limit cycles of piecewise
 linear differential centers separated by a conic.differential centers 
 separated by a conic
 
Submitted March 20, 2019. Published May 07, 2020.
Math Subject Classifications: 34C05, 34C07, 37G15.
Key Words: Discontinuous piecewise linear differential centers; limit cycles; conics.