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Boundedness and periodicity of solutions of certain fourth-order differential equations

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Summary

In this paper Ezeilo's result[2] on the boundedness of solution of a certain fourth-order equation is extended to more general equations of the form1.1(1). A much shorther proof of an earlier existence result[6] for periodic solutions of1.1(1) is also given.

References

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    J. O. C. Ezeilo,On the boundedness and the Stability of Solutions of Some fourth-order equations, J. Math. Analysis and Applications, Vol. 5, No 1, August, (1962).

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    -- --,An elementary proof of a Boundndness Theorem for a certain third-order equation; J. Lond. Math. Soc. (1963), pp. 11–16.

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    H. Shaefer, Math. Ann., 129, (1955), pp. 415–416.

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    H. O. Tejumola andJ. O. C. Ezeilo,On the existence of periodic Solutions of certain fourth order differential Equations; (To appear).

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    —— ——,Boundedness and Periodicity of Solutions of a certain system of third-order equations, Ann. Math. Pura. Appl. IV, Vol. LXXIV, (1966), pp. 283–316.

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    T. Yoshizawa, Mem. Univ. Kyoto, Series A, 28, (1953), pp. 133–141.

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Tejumola, H.O. Boundedness and periodicity of solutions of certain fourth-order differential equations. Annali di Matematica 80, 177–196 (1968). https://doi.org/10.1007/BF02413628

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Keywords

  • Differential Equation
  • Periodic Solution
  • General Equation
  • Existence Result
  • Early Existence