The equation x′=A(t)x+f(t, x, ε) is investigated for periodic solutions in the critical case. Explicit estimates for the existence region in ε for these solutions are obtained by employing implicit function theorem techniques.
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This paper is based on a Ph. D. thesis rubmitted by the authour to the faculty of the Graduate School of the University of Minnesota. The research was paid for in part by U. S. Army Research Contract No. DA-ARO-D-31-124G737.
Entrata in Redazione il 15 febbraio 1971.
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Freedman, H.I. Estimates on the existence region for periodic solutions of equations involving a small parameter. Il: Critical cases. Annali di Matematica 90, 259–279 (1971) doi:10.1007/BF02415051
- Periodic Solution
- Small Parameter
- Implicit Function Theorem
- Critical Case
- Explicit Estimate