L2-Solutions of y" = q (t) y and a Functional Equation
A Liapunov-type inequality for a class of third order delay-differential equations is derived.
Some asymptotic properties of principal solutions of the half-linear differential equation
We study planar polynomial differential equations with homogeneous components. This kind of equations present a simple and well known dynamics when the degrees (n and m) of both components coincide. Here we consider the case and we show that the dynamics is more complicated. In fact, we prove that such systems can exhibit periodic orbits only when nm is odd. Furthermore, for nm odd we give examples of such differential equations with at least (n+m)/2 limit cycles.