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Quantifying Poincaré’s continuation method for nonlinear oscillators. (English) Zbl 1433.34054

Summary: In the sixties, W. S. Loud obtained interesting results of continuation on periodic solutions in driven nonlinear oscillators with small parameter [Mem. Am. Math. Soc. 47, 133 p. (1964; Zbl 0128.31802)]. In this paper Loud’s results are extended out for periodically driven Duffing equations with odd symmetry quantifying the continuation parameter for a periodic odd solution which is elliptic and emanates from the equilibrium of the nonperturbed problem.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34D10 Perturbations of ordinary differential equations

Citations:

Zbl 0128.31802

References:

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