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New non-standard Lagrangians for the Liénard-type equations. (English) Zbl 1356.34045
In the paper under review, the authors obtain non-standard Lagrangians for some Liénard-type equations. For the proof, the authors use generalized Sundman transformations to transform the equations into either damped harmonic oscillator or of the Painlevé-Gambiér type, which admits non-standard Lagrangians.

MSC:
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
70H03 Lagrange’s equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
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