A version of Sharkovskii's theorem for differential equations |
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Authors: | Jan Andres Karel Pastor |
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Institution: | Department of Mathematical Analysis, Faculty of Science, Palacky University, Tomkova 40, 779~00 Olomouc-Hejcín, Czech Republic ; Department of Mathematical Analysis, Faculty of Science, Palacky University, Tomkova 40, 779~00 Olomouc-Hejcín, Czech Republic |
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Abstract: | We present a version of the Sharkovskii cycle coexistence theorem for differential equations. Our earlier applicable version is extended here to hold with the exception of at most two orbits. This result, which (because of counter-examples) cannot be improved, is then applied to ordinary differential equations and inclusions. In particular, if a time-periodic differential equation has -periodic solutions with , for all , then infinitely many subharmonics coexist. |
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Keywords: | Sharkovskii's theorem applicable (multivalued) version $M$-maps (primary) orbits translation operators subharmonics multiplicity results |
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