TITLE:
Periodic Solutions of Some Polynomial Differential Systems in R4
AUTHORS:
Makhlouf Amar, Bousbiat Lilia
KEYWORDS:
Periodic Solution, Averaging Theory, Differential System
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.1,
January
26,
2017
ABSTRACT: We provide sufficient conditions for the existence of periodic solutions of the polynomial fourth order differential system , where A is a 4 × 4 constant matrix, P1, P2, P3 and P4 are polynomials in the variables x, y, u, v of degrees n, hi(t) = hi(t + 2π) with i = 1, 2, 3, 4 being periodic functions and ε is a small parameter.