Remarks on Barbashin–Ezeilo Problem on third-order nonlinear differential equations

In this paper, we use the frequency domain criteria to initiate a general result on the Barbashin–Ezeilo Problem on third-order nonlinear differential equation. Earlier ideas of Burkin [I.M. Burkin, Orbital stability of second-kind limiting cycles for dynamical systems with cylindrical phase space, Differential Equations 29 (1993) 1262–1264], Leonov [G.A. Leonov, A frequency criterion for the existence of limit cycles of dynamical systems with cylindrical phase spaces, Differential Equations 23 (1987) 1375–1378] on the problem are being improved upon.