Applying the averaging theory of first and second order to a class of generalized polynomial Liénard differential equations, we improve the known lower bounds for the maximum number of limit cycles… (More)

One of themain problems in the theory of differential systems is the study of their periodic orbits, their existence, their number, and their stability. As usual, a limit cycle of a differential… (More)

We provide sufficient conditions for the existence of periodic solutions of the third–order differential equations u′′′ + (a1u + a0)u′′ + (b1u + b0)u′ + c2u + a0b0u = εF (t, u, u′, u′′, ε), where a0,… (More)

We provide sufficient conditions for the existence of periodic solutions of the fourth-order differential equation .... x + (1 + p)ẍ+ px = ǫF (t, x, ẋ, ẍ, ... x ), where p = p1/p2 with p1, p2 ∈ N and… (More)

We apply the averaging theory of third order to polynomial quadratic vector fields in R to study the Hopf bifurcation occurring in that polynomial. Our main result shows that at most 10 limit cycles… (More)

whereP(x, y) andQ(x, y) are arbitrary polynomials of degree n starting with terms of degree 2, a is a real parameter, and ε is small parameter.They proved that for ε ̸ = 0 sufficiently small, the… (More)

We provide sufficient conditions for the existence of periodic solutions of the second order Hamiltonian system −x′′ − λx = εV ′ x (t, x) , where ε is a small parameter, x ∈ R and V (t, x) is… (More)