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Asymptotic behavior of the solutions of the third order nonlinear differential equationsu‴±tσ u n =0u n =0

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Summary

The asymptotic behavior of the proper nonoscillator solutions of the nonlinear, third order, ordinary differential equation(*) u′″±tσun=0, where n>1 and σ is an arbitrary real number, is considered. Cases for σ and n are studied and the possible asymptotic behavior (t→∞) of the solutions of(*) are found and conditions for their existence are demonstrated.

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This paper is part of the author's dissertation which was prepared under the dirrection of ProfessorThomas G. Hallam at Florida State University. This research was supported by NSF grant GP 11534.

Entrata in Redazione il 9 maggio 1973.

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Ohme, P.A. Asymptotic behavior of the solutions of the third order nonlinear differential equationsu‴±tσ u n =0u n =0. Annali di Matematica 104, 43–65 (1975). https://doi.org/10.1007/BF02417010

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Keywords

  • Differential Equation
  • Real Number
  • Ordinary Differential Equation
  • Asymptotic Behavior
  • Nonoscillator Solution