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Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities

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Abstract

We present results on the existence of oscillating solutions of specific form (“quasiperiodic solutions) for a nonlinear differential equation with power nonlinearity. For oscillating solutions to third-order equations of this type, we obtain an asymptotics of extremums, which is expressed through the asymptotics of extremums of a “quasiperiodic” solution. These results clarify the asymptotic formulas for the modules of extremums of solutions obtained by the author earlier.

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References

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    I. V. Astashova

  2. G. V. Plekhanov Russian University of Economics, Moscow, Russia

    I. V. Astashova

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  1. I. V. Astashova
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Correspondence to I. V. Astashova.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 132, Proceedings of International Symposium “Differential Equations–2016,” Perm, 2016.

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Astashova, I.V. Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities. J Math Sci 230, 651–655 (2018). https://doi.org/10.1007/s10958-018-3762-8

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  • DOI: https://doi.org/10.1007/s10958-018-3762-8

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