Guiding functions and periodic solutions to functional-differential equations
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- by Alessandro Fonda PDF
- Proc. Amer. Math. Soc. 99 (1987), 79-85 Request permission
Abstract:
A new definition of a guiding function for functional differential equations is given, which is sometimes better for applications than the known one by Mawhin. We then prove an existence result for periodic solutions of FDEs related to the new definition.References
- G. Dylawerski and L. Górniewicz, A remark on the Krasnosiel′skiĭ’s translation operator along trajectories of ordinary differential equations, Serdica 9 (1983), no. 1, 102–107. MR 725816
- Robert E. Gaines and Jean L. Mawhin, Coincidence degree, and nonlinear differential equations, Lecture Notes in Mathematics, Vol. 568, Springer-Verlag, Berlin-New York, 1977. MR 0637067, DOI 10.1007/BFb0089537
- M. A. Krasnosel′skiĭ, The operator of translation along the trajectories of differential equations, Translations of Mathematical Monographs, Vol. 19, American Mathematical Society, Providence, R.I., 1968. Translated from the Russian by Scripta Technica. MR 0223640 —, An alternative principle for establishing the existence of periodic solutions of differential equations with a lagging argument, Soviet Math. Dokl. 4 (1963), 1412-1415.
- M. A. Krasnosel′skiĭ and P. P. Zabreĭko, Geometricheskie metody nelineĭ nogo analiza, Nelineĭnyĭ Analiz i ego Prilozheniya. [Monographs in Nonlinear Analysis and Applications], Izdat. “Nauka”, Moscow, 1975 (Russian). MR 0500310
- A. Lasota and James A. Yorke, Bounds for periodic solutions of differential equations in Banach spaces, J. Differential Equations 10 (1971), 83–91. MR 279411, DOI 10.1016/0022-0396(71)90097-0
- J. Mawhin, Periodic solutions of nonlinear functional differential equations, J. Differential Equations 10 (1971), 240–261. MR 294823, DOI 10.1016/0022-0396(71)90049-0 —, Topological degree methods in nonlinear boundary value problems, CBMS Regional Conf. Ser. in Math., no. 40, Amer. Math. Soc., Providence, R. I., 1977. —, Nonlinear perturbations of Fredholm mappings in normal spaces and applications to differential equations, Trabalho Mat., no. 61, Univ. Brasilia, 1974.
- Roger D. Nussbaum, Periodic solutions of analytic functional differential equations are analytic, Michigan Math. J. 20 (1973), 249–255. MR 322315
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 79-85
- MSC: Primary 34C25; Secondary 34K15
- DOI: https://doi.org/10.1090/S0002-9939-1987-0866434-X
- MathSciNet review: 866434