کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417052 | 1338514 | 2016 | 27 صفحه PDF | دانلود رایگان |
We consider perturbed pendulum-like equations on the cylinder of the form x¨+sinâ¡(x)=εâs=0mQn,s(x)xËs where Qn,s are trigonometric polynomials of degree n, and study the number of limit cycles that bifurcate from the periodic orbits of the unperturbed case ε=0 in terms of m and n. Our first result gives upper bounds on the number of zeros of its associated first order Melnikov function, in both the oscillatory and the rotary regions. These upper bounds are obtained expressing the corresponding Abelian integrals in terms of polynomials and the complete elliptic functions of first and second kind. Some further results give sharp bounds on the number of zeros of these integrals by identifying subfamilies which are shown to be Chebyshev systems.
Journal: Journal of Differential Equations - Volume 261, Issue 3, 5 August 2016, Pages 2141-2167