Summary
In a recent paper[1] Ezeilo considered the nonlinear third order differential equation x‴ + ω(x′)x″ + ω(x)x′ + ϑ(x, x′, x″)=p(t). He proved the ultimate boundedness of the solutions on rather general conditions for the nonlinear terms ϕ, ϕ, ϑ. These conditions (in a little weaker form) are also sufficient in order to prove the existence of forced oscillations in the case when the excitation is ω-periodic. For this purpose the Lerag-Schauder principle in a form suggested by G. Güssefeldt[2] is applicable.
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Dedicated to ProfessorKarl Klotter on his 70th birthday
Entrata in Redazione il 21 ottobre 1971.
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Reissig, R. An extension of Ezeilo's result. Annali di Matematica 92, 199–209 (1972). https://doi.org/10.1007/BF02417947
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DOI: https://doi.org/10.1007/BF02417947