On Truly Nonlinear Oscillator Equations of Ermakov-Pinney Type

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DOI: https://doi.org/10.28924/2291-8639-19-2021-970
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Marcellin Nonti, Kolawole Kegnide Damien Adjai, Jean Akande, Marc Delphin Monsia, On Truly Nonlinear Oscillator Equations of Ermakov-Pinney Type, Int. J. Anal. Appl., 19 (6) (2021), 970-983.

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Marcellin Nonti, Kolawole Kegnide Damien Adjai, Jean Akande, Marc Delphin Monsia

Abstract

In this paper we present a general class of differential equations of Ermakov-Pinney type which may serve as truly nonlinear oscillators. We show the existence of periodic solutions by exact integration after the phase plane analysis. The related quadratic Lienard type equations are examined to show for the first time that the Jacobi elliptic functions may be solution of second-order autonomous non-polynomial differential equations.

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