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On Topological Properties of the Set of Solutions of Operator Inclusions with a Multi-Valued Lipschitz Right-Hand Side

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Abstract

This paper is devoted to the study of the topological dimension of the set of solutions of the operator inclusion of the form \(A(x)\in\lambda F(x)\), where A is a bounded linear surjective operator, and F is a multi-valued Lipschitz map with closed convex images. The resulting theorem establishes a connection between the dimension of the kernel of the operator A and the dimension of the set of solutions of this inclusion.

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REFERENCES

  1. Ricceri, B. "On the topological dimension of the solution set of a class of nonlinear equations", C.R. Acad. Sci., Paris 325, 65-70 (1997).

    Article  MathSciNet  Google Scholar 

  2. Gel'man, B.D. "On a Class of Operator Equations", Math. Notes 70 (4), 494-501 (2001).

    Article  MathSciNet  Google Scholar 

  3. Gel'man, B.D. "Operator equations and Cauchy problem for degeneration differential equations", Proceedings of Voronezh State University, Ser.: Phys. Math. 2, 86-91 (2007) [in Russian].

    Google Scholar 

  4. Nadler, S.B. "Multi-valued contraction map**s", Pasif. J. Math. 30, 475-488 (1969).

    Article  MathSciNet  Google Scholar 

  5. Borisovich, Yu.G., Gel'man, B.D., Myshkis, A.D., Obukhovskii, V.V. Introduction to the theory of multi-valued map**s and differential inclusions («Librokom», Moscow, 2016 ) [in Russian].

    MATH  Google Scholar 

  6. Gel'man, B.D. "Multi-valued contractive map**s and their applications", Proceedings of Voronezh State University, Ser.: Phys. Math. 1, 74-86 (2009) [in Russian].

    Google Scholar 

  7. Saint Raymond, J. "Multivalued contractions", Set-Valued Anal. 2, 559-571 (1994).

    Article  MathSciNet  Google Scholar 

  8. Ricceri, B. "Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque á valeurs convexes", Atti Accad. Nas. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 81, 283-286 (1987).

    MATH  Google Scholar 

  9. Arutyunov, A.V., Gel'man, B.D. "On the structure of the set of coincidence points", Sb. Math. 206 (3), 370-388 (2015).

    Article  MathSciNet  Google Scholar 

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Funding

This work was funded by the Russian Foundation for Basic Research, project no. 19-01-00080.

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Authors and Affiliations

  1. Voronezh State University, 1 Universitetskaya sq., 394018, Voronezh, Russia

    B. D. Gel’man

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  1. B. D. Gel’man
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Correspondence to B. D. Gel’man.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 5, pp. 11–15.

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Gel’man, B.D. On Topological Properties of the Set of Solutions of Operator Inclusions with a Multi-Valued Lipschitz Right-Hand Side. Russ Math. 65, 4–7 (2021). https://doi.org/10.3103/S1066369X21050029

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  • DOI: https://doi.org/10.3103/S1066369X21050029

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