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...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.展开更多
We study the limit cycles of wide classes of perturbed Li′enard equations, which can be seen as a particular perturbation of the harmonic oscillator, using the averaging theory. We illustrate this study with many app...We study the limit cycles of wide classes of perturbed Li′enard equations, which can be seen as a particular perturbation of the harmonic oscillator, using the averaging theory. We illustrate this study with many applications.展开更多
文摘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.
文摘We study the limit cycles of wide classes of perturbed Li′enard equations, which can be seen as a particular perturbation of the harmonic oscillator, using the averaging theory. We illustrate this study with many applications.
