On a multivalued version of the Sharkovskii theorem and its application to differential inclusions, III
Keywords
Sharkovskiĭ theorem, multivalued version, multidimensional version, linear continuum setting, infinitely many orbits, subharmonics of differential systemsAbstract
An extension of the celebrated Sharkovskiĭ cycle coexisting theorem (see [< i> Coexistence of cycles of a continuous map of a line into itself< /i> , Ukrain. Math. J. < b> 16< /b> (1964), 61–71]) is given for (strongly) admissible multivalued self-maps in the sense of [L. Górniewicz, < i> Topological Fixed Point Theory of Multivalued Mappings< /i> , Kluwer, Dordrecht, 1999], on a Cartesian product of linear continua. Vectors of admissible self-maps have a triangular structure as in [[P. E. Kloeden, < i> On Sharkovsky’s cycle coexisting ordering< /i> , Bull. Austral. Math. Soc. < b> 20< /b> (1979), 171–177]. Thus, we make a joint generalization of the results in [J. Andres, J. Fišer and L. Jüttner, < i> On a multivalued version of the Sharkovskiĭ theorem and its application to differential inclusions< /i> , Set-Valued Anal. < b> 10< /b> (2002), 1–14], [J. Andres and L. Jüttner, < i> Period three plays a negative role in a multivalued version of Sharkovskiĭ’s theorem< /i> , Nonlinear Anal. < b> 51< /b> (2002), 1101–1104], [J. Andres, L. Jüttner and K. Pastor, < i> On a multivalued version of the Sharkovskiĭ theorem and its application to differential inclusions II< /i> ] (a multivalued case), in [P. E. Kloeden, < i> On Sharkovsky’s cycle coexisting ordering< /i> , Bull. Austral. Math. Soc. < b> 20< /b> (1979), 171–177] (a multidimensional case), and in [H. Schirmer, < i> A topologist’s view of Sharkovskiĭ’s theorem< /i> , Houston, J. Math. < b> 11< /b> (1985), 385–395] (a linear continuum case). The obtained results can be applied, unlike in the single-valued case, to differential equations and inclusions.Downloads
Published
2003-12-01
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1.
ANDRES, Jan and PASTOR, Karel. On a multivalued version of the Sharkovskii theorem and its application to differential inclusions, III. Topological Methods in Nonlinear Analysis. Online. 1 December 2003. Vol. 22, no. 2, pp. 369 - 386. [Accessed 29 March 2024].
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