In this paper, we prove smoothness of bifurcation function for a piecewise smooth periodic
equation, and then use the bifurcation function together with its smoothness to study the …

It is known that the Melnikov function method is equivalent to the averaging method for
studying the number of limit cycles of planar analytic (or C∞) near-Hamiltonian differential …

In this paper, we consider the quadratic isochronous centers perturbed inside piecewise
polynomial differential systems of arbitrary degree n with the straight line of discontinuity x …

In our previous work, we have studied the limit cycles for a class of discontinuous piecewise
quadratic polynomial differential systems with a non-regular line of discontinuity, which is …

This paper deals with the problem of limit cycle bifurcations for a piecewise smooth Hamilton
system with two straight lines of separation. By analyzing the obtained first order Melnikov …

In this paper we study the limit cycles which bifurcate from the periodic orbits of the quadratic
uniform isochronous center x ̇=− y+ xy, y ̇= x+ y 2, when this center is perturbed inside the …

This paper presents new results on the limit cycles of a Liénard system with symmetry
allowing for discontinuity. Our results generalize and improve the results in [32, Theorem 1 …

In this paper we study the maximal number of limit cycles for a class of piecewise smooth
near-Hamiltonian systems under polynomial perturbations. Using the second order …

The present paper is devoted to study the problem of limit cycle bifurcations for nonsmooth
integrable differential systems with two perpendicular switching lines. By using the Picard …

In the study of the weakened Hilbert's 16th problem, there usually appears period annulus
surrounding more than one singular point, implying that there are often more than three …