The dissipativity of systems of ordinary differential equations in the plane

Moscow University Mathematics Bulletin, 43 (1988) 4, 93-96, MR 90b:34047.

The results deal with the existence of a periodic solution and the ultimate boundedness of the trajectories of systems of ordinary differential equations, in particular the Lienard x''+f(x,x')x'+g(x)=e(t,x,x') and Rayleigh x"+f(x')+g(x)=e(t,x,x') equations. The results have been developed further in The dissipativity of the generalized Lienard equation and Dissipativity in the plane.