Abstract.
We discuss the genericity of some multiplicity results for periodically perturbed autonomous first- and second-order ODEs on manifolds.¶In particular, the genericity of the following property is investigated: if the differentiable manifold M is compact, then the equation \(\ddot{x}\) π=h(x,\(\dot{x}\))+f(t,x,\(\dot{x}\)) on M has |χ(M)| geometrically distinct T-periodic solutions for any small enough T-periodic perturbing function f.
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Received: January 24, 2000; in final form: January 16, 2001¶Published online: March 19, 2002
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Lewicka, M., Spadini, M. A remark on the genericity of multiplicity results for forced oscillations on manifolds. Ann. Mat. Pura Appl. IV. Ser. 181, 85–94 (2002). https://doi.org/10.1007/s102310200030
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DOI: https://doi.org/10.1007/s102310200030