## Summary

The asymptotic behavior of the proper nonoscillator solutions of the nonlinear, third order, ordinary differential equation*(*)* u′″±t^{σ}u^{n}=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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## Author information

### Affiliations

## Additional information

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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### Cite this article

Ohme, P.A. Asymptotic behavior of the solutions of the third order nonlinear differential equations*u*‴±t^{σ}
*u*
_{
n
}=0*u*
_{
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