Previous article Next article Estimates on the Existence Region for Periodic Solutions of Equations Involving a Small Parameter I: the Noncritical CaseH. I. FreedmanH. I. Freedmanhttps://doi.org/10.1137/0116113PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. D. Birkhoff and , D. C. Lewis, On the periodic motions near a given periodic motion of a dynamical system, Ann. Mat., Pura Appl., 12 (1633), 117–133 0007.37104 CrossrefGoogle Scholar[2] Earl A. Coddington and , Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955xii+429 MR0069338 0064.33002 Google Scholar[3] E. Goursat, Cours d'analyse mathematique, Vol. 1, Gauthier-Villars, Paris, 1910 Google Scholar[4] Daniel C. Lewis, Jr., Invariant Manifolds Near an Invariant Point of Unstable Type, Amer. J. Math., 60 (1938), 577–587 MR1507339 0019.06501 CrossrefGoogle Scholar[5] D. C. Lewis, Periodic solutions of differential equations containing a parameter, Duke Math. J., 22 (1955), 39–56 10.1215/S0012-7094-55-02205-5 MR0070806 0068.30006 CrossrefISIGoogle Scholar[6] D. C. Lewis, On the perturbation of a periodic solution when the variational system has non-trivial periodic solutions, J. Rational Mech. Anal., 4 (1955), 795–815 MR0073012 0068.30103 ISIGoogle Scholar[7] Yu. A. Ryabov, Estimations of the convergence region of periodic series representing solutions of differential equations involving a small parameter, Dokl. Akad. Nauk SSSR (N.S.), 118 (1958), 642–645 MR0097595 0079.30102 Google Scholar[8] Aurel Wintner, On implicit analytic systems, Comment. Math. Helv., 23 (1949), 294–302 MR0032781 0035.17201 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Persistence and extinction in a mathematical model of cell populations affected by radiationPeriodica Mathematica Hungarica, Vol. 56, No. 1 | 6 March 2008 Cross Ref Estimates on the Existence Regions of Perturbed Periodic SolutionsSIAM Journal on Mathematical Analysis, Vol. 9, No. 5 | 1 August 2006AbstractPDF (1195 KB)Periodic Solutions For ẋ = Ax + G(x, t) + ∊p(t)Canadian Mathematical Bulletin, Vol. 14, No. 4 | 20 November 2018 Cross Ref Estimates on the existence region for periodic solutions of equations involving a small parameter. Il: Critical casesAnnali di Matematica Pura ed Applicata, Vol. 90, No. 1 | 1 Dec 1971 Cross Ref Volume 16, Issue 6| 1968SIAM Journal on Applied Mathematics1123-1403 History Submitted:18 September 1967Published online:12 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0116113Article page range:pp. 1341-1349ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics