A recent result of Mawhin  concerning the existence of forced oscillations for a second order equation of Liénard type with an arbitrary damping term is extended to some cases where the restoring force is not assumed to be sufficiently weak. The results are valid, too, for a certain class of third order equations. They are based on the Leray-Schauder principle. By an analogous argumentation the Rayleigh equation with a quasilinear restoring force, but with an arbitrary damping term, is shown to possess a periodic solution. Again, the result admits an extension to a third order equation.
Periodic Solution Recent Result Order Equation Forced Oscillation Analogous Argumentation
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