Periodic solutions of a third order nonlinear differential equation

Summary The differential equation x‴ + ϕ(x′)x″ + ϕ(x)x′ + f(x)=p(t) is considered where the forcing term p is an ω-periodic function of t. In the special cases ϕ(x)=k² respectively ϕ(x′)=a the existence of periodic solutions is proved on the basis of the Lerag-Schauder fixed point technique. The conditions imposed on the nonlinear terms do not include the ultimate boundedness of all solutions. Entrata in Redazione il 18 settembre 1971.