Étude des cycles limites de certaines classes d'équation différentielles ordinaires perturbées du quatrième ordre

Abstract

Abstract We study the existence and number of limit cycles for two classes of fourthorder di¤erential equations using …rst-order averaging theory. The …rst class studied is non-autonomous of the form .... x + (1 + p2)•x + p2x = "F (t; x; _x; •x; ... x) where p is a rational number, " is a small real parameter and F is a function of class C2and T-periodic in t. The second class is autonomous of the form .... x + (1 + p2)•x + p2x = "F (x; _x; •x; ... x) where p is a rational number, " is a small real parameter and F is a function of class C2.