| Full text | |
| Author(s): |
Llibre, Jaume
;
Mereu, Ana Cristina
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Electronic Journal of Differential Equations; v. N/A, p. 8-pg., 2013-09-03. |
| Abstract | |
We divide R-2 into sectors S-1, ... , S-l, with l > 1 even, and define a discontinuous differential system such that in each sector, we have a smooth generalized Lienard polynomial differential equation (sic) + f(i) (x)(x) over dot + g(i) (x) = 0, i = 1, 2 alternatively, where f(i) and g(i) are polynomials of degree n - 1 and m respectively. Then we apply the averaging theory for first-order discontinuous differential systems to show that for any n and m there are non-smooth Lienard polynomial equations having at least max {n; m} limit cycles. Note that this number is independent of the number of sectors. Roughly speaking this result shows that the non-smooth classical (m = 1) Lienard polynomial differential systems can have at least the double number of limit cycles than the smooth ones, and that the non-smooth generalized Lienard polynomial differential systems can have at least one more limit cycle than the smooth ones. (AU) | |
| FAPESP's process: | 12/20884-8 - Periodic orbits in non-smooth systems |
| Grantee: | Ana Cristina de Oliveira Mereu |
| Support Opportunities: | Scholarships abroad - Research |