In this paper, the number and distributions of limit cycles bifurcating from a double
homoclinic loop and a double heteroclinic loop of piecewise smooth systems with three …

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 develop an arbitrary order Melnikov function to study limit cycles bifurcating
from a periodic submanifold for autonomous piecewise smooth differential systems in R n …

We study the family of piecewise linear differential systems in the plane with two pieces
separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number …

In this paper, we are interested in providing lower estimations for the maximum number of
limit cycles H (n) that planar piecewise linear differential systems with two zones separated …

In this paper, we study limit cycle bifurcations near homoclinic and heteroclinic loops in
piecewise smooth systems with three zones separated by two parallel straight lines. By …

In this paper, we consider a perturbation of planar general piecewise Hamiltonian systems
with nonregular separation line. A general explicit expression of the first and second order …

This paper aims to study the limit cycles of planar piecewise polynomial Hamiltonian
systems of degree n with the switching boundary y= xm, where m and n are positive …

In this paper, we study the limit cycles for m-piecewise discontinuous polynomial Liénard
differential systems of degree n with m/2 straight lines passing through the origin whose …

The second part of Hilbert's sixteenth problem consists in determining the upper bound H (n)
for the number of limit cycles that planar polynomial vector fields of degree n can have. For …