Limit cycles for M-piecewise discontinuous polynomial Li,nard differential equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)We provide lower bounds for the maximum number of limit cycles for the m-piecewise discontinuous polynomial differential equations , , where the zero set of the function sgn(g (m) (x, y)) with m = 2, 4, 6, . . . is the product of m/2 straight lines passing through the origin of coordinates dividing the plane into sectors of angle 2 pi/m, and sgn(z) denotes the sign function.We provide lower bounds for the maximum number of limit cycles for the m-piecewise discontinuous polynomial differential equations , , where the zero set of the function sgn(g (m) (x, y)) with m = 2, 4, 6, . . . is the product of m/2 straight lines passin6615166FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)FAPESP [2007/06896-5]CAPES [PHB-2009-0025-PC]2009-0025-P