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Topological approach to random diferential inclusions

Yıl 2020, Cilt: 3 Sayı: 4, 196 - 206, 30.12.2020

Öz

In the present paper random multivalued admissible operators are considered. First for such operators
we shall formulate the following topological results: Schauder-type Fixed Point Theorems, Leray?Schauder
Alternative, Granas Continuation Method and Topological Degree.
Next these problems will be transformed to the existence problems, periodic problems and implicit
problems for random di?erentuial inclusions.
Let us remark that this paper constitute a summary and complement of the following earlier papers:
[2], [3], [5], [6], [10], [11], [14] and [15]. This work can be considered as an advanced survey with some new
results: mainly concerning the theory of random di?erential inclusions. We believe that this paper will be
useful for mathematiciants and students intrested in topological methods of nonconvex analysis.

Kaynakça

  • 1] J. Andres, L. Górniewicz, Topological Fixed Point Principles for Boundary Value Problems, Kluwer, 2003.
  • [2] J. Andres, L. Górniewicz, Random topological degree and random di?erential inclusions, Topol. Methods Nonlinear Anal. 40 (2012), 337-358.
  • [3] J. Andres , L. Górniewicz, Implicit diferential inclusions with acyclic right-hand sides an essential fixed point approach, Dyn. Syst. 26 (2017), 237-258.
  • [4] T.D. Benavides, G.L. Acedo, H.K. Xu, Random fixed points of set valued mappings, Proc. Amer. Math. Soc. 124 (1996), 431-438.
  • [5] R. Bielawski, L. Górniewicz, Some applications of the Leray-Schauder alternative to diferential equations, NATO ASI Series Ser. C Math. Phys. Ser., Vol. 173, edited by S.P. Singh, 187-194.
  • [6] R. Bielawski, L. Górniewicz, A fixed point approach to di?erential equations, Lecture Notes in Math., Vol. 1411, Springer, Berlin, 1989, 9-14.
  • [7] R. Bielawski, L. Górniewicz, S. Plaskacz, Topological approach to diferential inclusions on closed subsets of R n , Dynamics Reported, 1 New Series, Springer, 1991, 225-250.
  • [8] F.S. De Blasi, L. Górniewicz, G. Pianigiani, Topological degree and periodic solutions of di?erential inclusions, Nonlinear Anal. 3 (1999), 217-245.
  • [9] F.S. De Blasi, J. Myjak, On the solution sets for diferential inclusions, Bull. Polon. Math. Soc. 12 (1985), 17-23.
  • [10] M. Frigon, L. Górniewicz, T. Kaczyski, Diferential inclusions and implicit equations on closed subset of euclidean n- dimensional space, Proceedings of the First WCNA, Tampa, Florida, W. de Gruyter, Berlin 1996, 1197-1206.
  • [11] G. Gabor, L. Górniewicz, M. ‘losarski, Generalized topological essentiality and coincidence points of multivalued mappings, Set-Valued Anal. 17 (2009), 1-19.
  • [12] L. Górniewicz, Topological structure of solution sets: current results, Arch. Math. 36 (2000), 343-382.
  • [13] L. Górniewicz, Topological Fixed Point Theory for Multivalued Mappings, Springer, 2006 (second edition).
  • [14] L. Górniewicz, O. Górniewicz, Topological essentiality of random w-admissible operators, Discuss. Math. 39 (2019), 123- 134. [15] L. Górniewicz, M. Slosarski, Topological essentiality and diferential inclusions, Bull. Aust. Math. Soc. 45 (1992), 177-193.
  • [16] A. Granas, The theory of compact vector fields and some of its applications, Dissertationes Math. 30 (1962), 1-93.
  • [17] A. Granas, J. Dugundji, Fixed Point Theory, Springer, 2003.
  • [18] N.S. Papageorgiou, Random fixed points and random diferential inclusions, Int. J. Math. Sci. 3 (1988), 551-560.
  • [19] L.E. Rybinski, Random fixed points and viable random solutions of functional diferential equations, J. Math. Anal. 142 (1989), 53-61.
  • [20] J.L. Strand, Random ordinary diferential equations, J. Diferential Equations 7 (1970), 538-553.
Yıl 2020, Cilt: 3 Sayı: 4, 196 - 206, 30.12.2020

Öz

Kaynakça

  • 1] J. Andres, L. Górniewicz, Topological Fixed Point Principles for Boundary Value Problems, Kluwer, 2003.
  • [2] J. Andres, L. Górniewicz, Random topological degree and random di?erential inclusions, Topol. Methods Nonlinear Anal. 40 (2012), 337-358.
  • [3] J. Andres , L. Górniewicz, Implicit diferential inclusions with acyclic right-hand sides an essential fixed point approach, Dyn. Syst. 26 (2017), 237-258.
  • [4] T.D. Benavides, G.L. Acedo, H.K. Xu, Random fixed points of set valued mappings, Proc. Amer. Math. Soc. 124 (1996), 431-438.
  • [5] R. Bielawski, L. Górniewicz, Some applications of the Leray-Schauder alternative to diferential equations, NATO ASI Series Ser. C Math. Phys. Ser., Vol. 173, edited by S.P. Singh, 187-194.
  • [6] R. Bielawski, L. Górniewicz, A fixed point approach to di?erential equations, Lecture Notes in Math., Vol. 1411, Springer, Berlin, 1989, 9-14.
  • [7] R. Bielawski, L. Górniewicz, S. Plaskacz, Topological approach to diferential inclusions on closed subsets of R n , Dynamics Reported, 1 New Series, Springer, 1991, 225-250.
  • [8] F.S. De Blasi, L. Górniewicz, G. Pianigiani, Topological degree and periodic solutions of di?erential inclusions, Nonlinear Anal. 3 (1999), 217-245.
  • [9] F.S. De Blasi, J. Myjak, On the solution sets for diferential inclusions, Bull. Polon. Math. Soc. 12 (1985), 17-23.
  • [10] M. Frigon, L. Górniewicz, T. Kaczyski, Diferential inclusions and implicit equations on closed subset of euclidean n- dimensional space, Proceedings of the First WCNA, Tampa, Florida, W. de Gruyter, Berlin 1996, 1197-1206.
  • [11] G. Gabor, L. Górniewicz, M. ‘losarski, Generalized topological essentiality and coincidence points of multivalued mappings, Set-Valued Anal. 17 (2009), 1-19.
  • [12] L. Górniewicz, Topological structure of solution sets: current results, Arch. Math. 36 (2000), 343-382.
  • [13] L. Górniewicz, Topological Fixed Point Theory for Multivalued Mappings, Springer, 2006 (second edition).
  • [14] L. Górniewicz, O. Górniewicz, Topological essentiality of random w-admissible operators, Discuss. Math. 39 (2019), 123- 134. [15] L. Górniewicz, M. Slosarski, Topological essentiality and diferential inclusions, Bull. Aust. Math. Soc. 45 (1992), 177-193.
  • [16] A. Granas, The theory of compact vector fields and some of its applications, Dissertationes Math. 30 (1962), 1-93.
  • [17] A. Granas, J. Dugundji, Fixed Point Theory, Springer, 2003.
  • [18] N.S. Papageorgiou, Random fixed points and random diferential inclusions, Int. J. Math. Sci. 3 (1988), 551-560.
  • [19] L.E. Rybinski, Random fixed points and viable random solutions of functional diferential equations, J. Math. Anal. 142 (1989), 53-61.
  • [20] J.L. Strand, Random ordinary diferential equations, J. Diferential Equations 7 (1970), 538-553.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Lech Górniewicz Bu kişi benim

Yayımlanma Tarihi 30 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 4

Kaynak Göster

APA Górniewicz, L. (2020). Topological approach to random diferential inclusions. Results in Nonlinear Analysis, 3(4), 196-206.
AMA Górniewicz L. Topological approach to random diferential inclusions. RNA. Aralık 2020;3(4):196-206.
Chicago Górniewicz, Lech. “Topological Approach to Random Diferential Inclusions”. Results in Nonlinear Analysis 3, sy. 4 (Aralık 2020): 196-206.
EndNote Górniewicz L (01 Aralık 2020) Topological approach to random diferential inclusions. Results in Nonlinear Analysis 3 4 196–206.
IEEE L. Górniewicz, “Topological approach to random diferential inclusions”, RNA, c. 3, sy. 4, ss. 196–206, 2020.
ISNAD Górniewicz, Lech. “Topological Approach to Random Diferential Inclusions”. Results in Nonlinear Analysis 3/4 (Aralık 2020), 196-206.
JAMA Górniewicz L. Topological approach to random diferential inclusions. RNA. 2020;3:196–206.
MLA Górniewicz, Lech. “Topological Approach to Random Diferential Inclusions”. Results in Nonlinear Analysis, c. 3, sy. 4, 2020, ss. 196-0.
Vancouver Górniewicz L. Topological approach to random diferential inclusions. RNA. 2020;3(4):196-20.