Abel-like differential equations with a unique limit cycle

作者：Alvarez M J; Bravo J L; Fernandez M^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(11): 3694-3702.

DOI：10.1016/j.na.2011.02.049

• Periodic solutions
• Abel equation

For the family of scalar Abel-like equations x' = A(t)x(n) + bB(t)x(m), where A(t) = Sigma(k)(l-1) a(l) sin(il) (t) cos(jl) (t), B(t) = sin(ib) (t) cos(ib) (t), a(l), b is an element of R, n, m, k, i(l), j(l), i(b), j(b) is an element of Z(+), n, m >= 2, and k >= 1, we characterize the existence of non-trivial limit cycles (periodic solutions that are isolated in the set of periodic solutions different from the trivial x(t) equivalent to 0) in terms of n, m, k, i(l), j(l), i(b), j(b).

• 出版日期2011-7