The original Hilbert's 16th problem can be split into four parts consisting of Problems A–D. In
this paper, the progress of study on Hilbert's 16th problem is presented, and the relationship …

The number of solutions of the Abel differential equation dx(t)/dt=A(t)x(t)^3+B(t)x(t)^2+C(t)x(t)
satisfying the condition x(0)=x(1) is studied, under the hypothesis that either A(t) or B(t) does …

×= P (x, y), ÿ= Q (x, y)(1) in which P and Q are polynomials. An account is given of some
recent work concerning the number of limit cycles of such systems and their relative …

We consider the class of polynomial differential equations x˙= λx+ Pn (x, y), y˙= λy+ Qn (x, y),
in R2 where Pn (x, y) and Qn (x, y) are homogeneous polynomials of degree n> 1 and λ≠ 0 …

In this paper we prove, that under certain hypotheses, the planar differential equation:˙ x= X1
(x, y)+ X2 (x, y),˙ y= Y1 (x, y)+ Y2 (x, y), where (Xi, Yi), i= 1, 2, are quasi-homogeneous vector …

This paper deals with the problem of finding upper bounds on the number of periodic
solutions of a class of one-dimensional nonautonomous differential equations: those with …

The paper deals with Hamiltonian systems with homogeneous nonlinearities. We prove that
such systems have no isochronous centers, that the period annulus of any of its centres is …

In this paper we study the limit cycles of the planar polynomial differential systems x˙= ax− y+
P n (x, y), y˙= x+ a y+ Q n (x, y), where P n and Q n are homogeneous polynomials of degree …

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 …

We study the class of vector fields of the form x= P 1 (x, y)+ P n (x, y), y= Q 1 (x, y)+ Q n (x, y),
where P k and Q k are real homogeneous polynomials of degree k, n⩾ 2, and the origin is a …