Annali di Matematica Pura ed Applicata

, Volume 92, Issue 1, pp 193–198 | Cite as

Periodic solutions of a third order nonlinear differential equation

  • Rolf Reissig


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.


Differential Equation Periodic Solution Nonlinear Term Nonlinear Differential Equation Force Term 
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Copyright information

© Nicola Zanichelli Editore 1972

Authors and Affiliations

  • Rolf Reissig
    • 1
  1. 1.Bochum

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