Limit cycles of continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center

<p style='text-indent:20px;'>Due to their applications many physical phenomena during these last decades the interest for studying continuous or discontinuous piecewise differential systems has increased strongly. The limit cycles play a main role in study of any planar system. Up now major part papers which have considered formed by two pieces separated one straight line.</p><p style='text-indent:20px;'>Here we consider parabola.</p><p style='text-indent:20px;'>We prove that parabola and linear center quadratic at most cycle. Moreover there are this class exhibiting So particular solved extension 16th Hilbert problem systems.</p>