Qualitative study of some classes of differential systems via Integrability

Abstract

This thesis is concerned by the occurrence of non trivial periodic solutions called limit cycles for polynomial differential systems in the real plane. This work splits into two major parts. In the first one, we have studied the existence and the number of limit cycles for two classes of planar differential systems of degrees four and seven respectively. The second part is concerned by the study of crossing limit cycles for a class of piecewise discontinuous differential systems separated by a straight line and formed by arbitrary linear and cubic parts with an isochronous center at the origin.