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On Implicit Differential Inclusions Generated by Orderly Covering Mappings

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Abstract

We study a differential inclusion unsolved for the derivative of the unknown function and prove a theorem on the solvability of an abstract inclusion generated by a multivalued orderly covering mapping. We use this result to obtain sufficient solvability conditions and estimate the solutions of the Cauchy problem for the implicit differential inclusion.

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References

  1. Kantorovich, L., The method of successive approximations for functional equations, Acta Math., 1939, vol. 71, pp. 63–97.

    Article  MathSciNet  Google Scholar 

  2. Krasnosel’skii, M.A., Polozhitel’nye resheniya operatornykh uravnenii (Positive Solutions of Operator Equations), Moscow: Gos. Izd. Fiz. Mat. Lit., 1962.

    Google Scholar 

  3. Azbelev, N.V., Izbrannye trudy (Selected Works), Ed. by Maksimov, V.P. and Rakhmatullina, L.F., Moscow; Izhevsk: Inst. Komp. Issled. 2012.

    Google Scholar 

  4. Zhukovskiy, E.S., On ordered-covering mappings and implicit differential inequalities, Differ. Equations, 2016, vol. 52, no. 12, pp. 1539–1556.

    Article  MathSciNet  MATH  Google Scholar 

  5. Granas, A. and Dugundji, J., Fixed Point Theory, New York: Springer-Verlag, 2003.

    Book  MATH  Google Scholar 

  6. Arutyunov, A.V., Zhukovskiy, E.S., and Zhukovskiy, S.E., Coincidence points principle for mappings in partially ordered spaces, Topology Appl., 2015, vol. 179, pp. 13–33.

    Article  MathSciNet  MATH  Google Scholar 

  7. Arutyunov, A.V., Zhukovskiy, E.S., and Zhukovskiy, S.E., Coincidence points principle for set-valued mappings in partially ordered spaces, Topology Appl., 2016, vol. 201, pp. 330–343.

    Article  MathSciNet  MATH  Google Scholar 

  8. Arutyunov, A.V., Zhukovskiy, E.S., and Zhukovskiy, S.E., On the well-posedness of differential equations unsolved for the derivative, Differ. Equations, 2011, vol. 47, no. 11, pp. 1541–1555.

    Article  MathSciNet  Google Scholar 

  9. Arutyunov, A.V., Avakov, E.R., and Zhukovskiy, S.E., Covering mappings and their applications to differential equations unsolved for the derivative, Differ. Equations, 2009, vol. 45, no. 5, pp. 627–649.

    Article  MathSciNet  MATH  Google Scholar 

  10. Arutyunov, A., de Oliveira, V.A., Pereira, F.L., Zhukovskiy, E., and Zhukovskiy, S., On the solvability of implicit differential inclusions, Appl. Anal., 2015, vol. 94, no. 1, pp. 129–143.

    Article  MathSciNet  MATH  Google Scholar 

  11. Arutyunov, A.V., Second-order conditions in extremal problems. The abnormal points, Trans. Amer. Math. Soc., 1998, vol. 350, no. 11, pp. 4341–4365.

    Article  MathSciNet  MATH  Google Scholar 

  12. Kolmogorov, A.N. and Fomin, S.V., Elementy teorii funktsii i funktsional’nogo analiza (Elements of Function Theory and Functional Analysis), Moscow: Nauka, 1972.

    Google Scholar 

  13. Borisovich, Yu.G., Gel’man, B.D., Myshkis, A.D., and Obukhovskii, V.V., Vvedenie v teoriyu mnogoznachnykh otobrazhenii i differentsial’nykh vklyuchenii (Introduction to Theory of Multivalued Mappings and Differential Inclusions), Moscow: URSS, 2011.

    Google Scholar 

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia, Moscow, 117198, Russia

    S. E. Zhukovskiy

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  1. S. E. Zhukovskiy
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Correspondence to S. E. Zhukovskiy.

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Russian Text © S.E. Zhukovskiy, 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 1, pp. 3–9.

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Zhukovskiy, S.E. On Implicit Differential Inclusions Generated by Orderly Covering Mappings. Diff Equat 55, 1–7 (2019). https://doi.org/10.1134/S0012266119010014

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  • DOI: https://doi.org/10.1134/S0012266119010014

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