TY - JOUR
T1 - Limit cycles of the generalized polynomial Liénard differential equations
AU - Mereu, Ana Cristina
AU - Teixeira, Marco Antonio
AU - Llibre, Jaume
PY - 2010/3/1
Y1 - 2010/3/1
N2 - 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. © 2009 Cambridge Philosophical Society.
AB - 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. © 2009 Cambridge Philosophical Society.
UR - https://dialnet.unirioja.es/servlet/articulo?codigo=3160368
U2 - 10.1017/S0305004109990193
DO - 10.1017/S0305004109990193
M3 - Article
SN - 0305-0041
VL - 148
SP - 363
EP - 383
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
ER -