Abstract
This paper establishes an existence and uniqueness theorem for quasiperiodic solution to nonlinear ordinary differential system with a perturbed term of the formdz/dt = U(t, z) + εF(t, z, ε) without passing through the notion of pseudoperiodic functions. A limitation of parameterε within which the theorem is valid can be given explicitly and a neighborhood of an approximate solution where the uniqueness of quasiperiodic solution is guaranteed also is given explicitly. The perturbed nonlinear oscillators such as Duffing type and Van der Pol type are studied.
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Ali, Z., Shinohara, Y., Imai, H. et al. Existence and uniqueness of quasiperiodic solutions to perturbed nonlinear oscillators. Japan J. Indust. Appl. Math. 15, 279 (1998). https://doi.org/10.1007/BF03167405
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DOI: https://doi.org/10.1007/BF03167405