On truly nonlinear oscillator equations of Ermakov-Pinney type, International Journal of Analysis and Applications - NONTI, Marcellin; ADJAÏ, K. K. Damien; Akande, Jean; MONSIA, MARC DELPHIN (My University, 2021)
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.
Keywords: Lienard equations; Ermakov-Pinney equation; truly nonlinear oscillators; periodic solution.