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L p-continuous selections of fixed points of multifunctions with decomposable values. III: Applications

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References

  1. A. A. Tolstonogov, “L p-Continuous selections of fixed points of multifunctions with decomposable values. I: Existence theorems,” Sibirsk. Mat. Zh.,40, No. 3, 695–709 (1999).

    MATH  MathSciNet  Google Scholar 

  2. A. A. Tolstonogov, “L p-Continuous selections of fixed points of multifunctions with decomposable values. II: Relaxation theorems,” Sibirsk. Mat. Zh.,40, No. 5, 1167–1181 (1999).

    MATH  MathSciNet  Google Scholar 

  3. F. Hiai and H. Umegaki, “Integrals, conditional expectations, and martingales of multivalued functions,” J. Multivariate Anal.,7, No. 1, 149–182 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  4. K. Kuratowski, Topology. Vol. 2 [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  5. R. Engelking, General Topology [Russian translation], Mir, Moscow (1986).

    Google Scholar 

  6. J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Univ. Press, New York (1985).

    MATH  Google Scholar 

  7. Ph. P. Clement, H. J. Heijmans, S. Angenent, C. J. van Duijn, and B. de Pagter, One-Parameter Semigroups. Abstract Differential Equations with Applications [Russian translation], Mir, Moscow (1992).

    Google Scholar 

  8. H. Tanabe, Equations of Evolution, Pitman, London (1979).

    MATH  Google Scholar 

  9. A. A. Tolstonogov and D. A. Tolstonogov, “L p-Continuous extreme selectors of multifunctions with decomposable values: Existence theorems,” Set-Valued Anal,4, No. 2, 173–203 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  10. A. Cellina, “On the set of solutions to Lipschitzean differential inclusions,” Differential Integral Equations,1, 495–500 (1988).

    MATH  MathSciNet  Google Scholar 

  11. A. Cellina and A. Ornelas, “Representation of the attainable set for Lipschitzean differential inclusions,” Rocky Mountain J. Math.,22, 117–124 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  12. A. Ornelas, “A continuous version of the Filippov-Gronwall inequality for differential inclusions,” Atti Acad. Naz. Lincei Rend. Cl. Ser. Fis. Mat. Natur.,1, 105–110 (1990).

    MATH  MathSciNet  Google Scholar 

  13. R. M. Colombo, A. Fryszkowski, T. Rzezuchowski, and V. Staicu, “Continuous selections of solution sets of Lipschitzean differential inclusions,” Funkcial. Ekvac.,34, 321–330 (1991).

    MATH  MathSciNet  Google Scholar 

  14. V. Staicu, “Continuous selection of solutions sets to evolution equations,” Proc. Amer. Math. Soc.,113, 403–413 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  15. V. Staicu and Wu He, “Arcwise connectedness of solution sets to Lipschitzean differential inclusions,” Boll. Un. Mat. Ital. (7),5A, 253–256 (1991).

    Google Scholar 

  16. V. Staicu, “On a non-convex hyperbolic differential inclusion,” Proc. Edinburgh Math. Soc. (2),35, 375–382 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  17. Z. Kannai, “Contraction-selection theorem and perturbed Lipschitz inclusions,” Pure Math. Appl.,4, 479–491 (1993).

    MATH  MathSciNet  Google Scholar 

  18. S. A. Marano, “Fixed points of multivalued contractions with nonclosed, nonconvex values,” Rend. Mat. Accad. Lincei,5, 203–212 (1994).

    MATH  MathSciNet  Google Scholar 

  19. F. S. De Blasi, G. Pianigiani, and V. Staicu, “Topological properties of nonconvex differential inclusions of evolution type,” Nonlinear Anal.,24, 711–720 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  20. F. S. De Blasi, G. Pianigiani, and V. Staicu, “On the solution sets of some nonconvex hyperbolic differential inclusions,” Czechoslovak Math. J.,120, 107–116 (1995).

    Google Scholar 

  21. V. V. Goncharov, “Some properties of viability problems depending on a parameter,” Nonlinear Differential Equations Appl.,2, 1–19 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  22. S. A. Marano and V. Staicu, “On the set of solutions to a class of nonconvex nonclosed differential inclusions,” Acta Math. Hungar.,76, No. 4, 287–301 (1997).

    Article  MATH  MathSciNet  Google Scholar 

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The research was financially supported by the Russian Foundation for Basic Research (Grant 96-01-00326).

Irkutsk. Translated fromSibirskiĭ Matematicheskiĭ Zhurnal, Vol. 40, No. 6, pp. 1380–1396, November–December, 1999.

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Tolstonogov, A.A. L p-continuous selections of fixed points of multifunctions with decomposable values. III: Applications. Sib Math J 40, 1173–1187 (1999). https://doi.org/10.1007/BF02677542

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