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Annali di Matematica Pura ed Applicata

, Volume 92, Issue 1, pp 199–209 | Cite as

An extension of Ezeilo's result

  • Rolf Reissig
Article

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.

Keywords

Differential Equation General Condition Nonlinear Term Weak Form Order Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

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    G. Güssefeldt,Zwei Methoden zum Nachweis von periodischen Lösungen bei gewöhnlichen Differentialgleichungen, Math. Nachr.,48 (1971), pp. 141–151.zbMATHMathSciNetGoogle Scholar
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Copyright information

© Nicola Zanichelli Editore 1972

Authors and Affiliations

  • Rolf Reissig
    • 1
  1. 1.Bochum

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