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… (More)

We provide lower bounds for the maximum number of limit cycles for the m–piecewise discontinuous polynomial differential equations ẋ = y + sgn(gm(x, y))F (x), ẏ = −x, where the zero set of the… (More)

In this paper we study piecewise linear differential systems formed by two regions separated by a straight line so that each system has a real saddle point in its region of definition. If both… (More)

In this paper, we provide a lower bound for the maximum number of limit cycles of planar discontinuous piecewise linear differential systems defined in two half-planes separated by a straight line.… (More)

The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise… (More)

We study a class of discontinuous piecewise linear differential systems with two zones separated by the straight line x = 0. In x > 0 we have a linear saddle with its equilibrium point living in x >… (More)

The goal of this work is to illustrate the explicit implementation of amethod for computing limit cycles which bifurcate from a continuum of isochronous periodic orbits forming a subset ofRn of… (More)

Abstract. We provide sufficient conditions for the existence of periodic solutions of the planar perturbed double pendulum with small oscillations having equations of motion θ̈1 = −2aθ1 + aθ2 +… (More)

We provide sufficient conditions por the existence of periodic solutions of some classes of autonomous and non–autonomous second order differential equations with discontinuous right–hand sides. In… (More)