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.
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Entrata in Redazione il 18 settembre 1971.
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Reissig, R. Periodic solutions of a third order nonlinear differential equation. Annali di Matematica 92, 193–198 (1972). https://doi.org/10.1007/BF02417946
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DOI: https://doi.org/10.1007/BF02417946