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.


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


Zbl 0128.31802
Full Text: DOI


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