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Period two implies all periods for a class of ODEs: A multivalued map approach |
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| Authors: | Jan Andres Tomá s Fü rst Karel Pastor |
| Affiliation: | Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc-Hejcín, Czech Republic ; Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc-Hejcín, Czech Republic ; Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc-Hejcín, Czech Republic |
| Abstract: | We present an elementary proof that, for a multivalued map  with nonempty connected values and monotone margins, the existence of a periodic orbit of any order  implies the existence of periodic orbits of all orders. This generalizes a very recent result of this type in terms of scalar ordinary differential equations without uniqueness, due to F. Obersnel and P. Omari, obtained by means of lower and upper solutions techniques. |
| Keywords: | Periodic orbits multivalued maps monotone margins Sharkovskii's theorem ordinary differential equations without uniqueness subharmonic solutions. |
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