Limit cycles of the generalized polynomial Liénard differential equations
Mathematical Proceedings of the Cambridge Philosophical Society, 2010•cambridge.org
We apply the averaging theory of first, second and third order to the class of generalized
polynomial Liénard differential equations. Our main result shows that for any n, m≥ 1 there
are differential equations of the form ẍ+ f (x) ẋ+ g (x)= 0, with f and g polynomials of degree
n and m respectively, having at least [(n+ m− 1)/2] limit cycles, where [·] denotes the integer
part function.
polynomial Liénard differential equations. Our main result shows that for any n, m≥ 1 there
are differential equations of the form ẍ+ f (x) ẋ+ g (x)= 0, with f and g polynomials of degree
n and m respectively, having at least [(n+ m− 1)/2] limit cycles, where [·] denotes the integer
part function.
We apply the averaging theory of first, second and third order to the class of generalized polynomial Liénard differential equations. Our main result shows that for any n, m ≥ 1 there are differential equations of the form ẍ + f(x)ẋ + g(x) = 0, with f and g polynomials of degree n and m respectively, having at least [(n + m − 1)/2] limit cycles, where [·] denotes the integer part function.
Cambridge University Press以上显示的是最相近的搜索结果。 查看全部搜索结果