TY - JOUR
T1 - Limit cycles for some abel equations having coefficients without fixed signs
AU - Bravo, J. L.
AU - FernÁndez, M.
AU - Gasull, A.
PY - 2009/1/1
Y1 - 2009/1/1
N2 - We prove that some 2π-periodic generalized Abel equations of the form x′ = A(t)xn + B(t)xm + C(t)x, with n ≠ m and n, m < 2 have at most three limit cycles. The novelty of our result is that, in contrast with other results of the literature, our hypotheses allow the functions A,B, and C to change sign. Finally we study in more detail the Abel equation x′ = A(t)x3 + B(t)x2, where the functions A and B are trigonometric polynomials of degree one. © 2009 World Scientific Publishing Company.
AB - We prove that some 2π-periodic generalized Abel equations of the form x′ = A(t)xn + B(t)xm + C(t)x, with n ≠ m and n, m < 2 have at most three limit cycles. The novelty of our result is that, in contrast with other results of the literature, our hypotheses allow the functions A,B, and C to change sign. Finally we study in more detail the Abel equation x′ = A(t)x3 + B(t)x2, where the functions A and B are trigonometric polynomials of degree one. © 2009 World Scientific Publishing Company.
KW - Abel equation
KW - Limit cycle
KW - Periodic solution
UR - https://www.scopus.com/pages/publications/77649157986
U2 - 10.1142/S0218127409025195
DO - 10.1142/S0218127409025195
M3 - Article
SN - 0218-1274
VL - 19
SP - 3869
EP - 3876
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 11
ER -