Random differential inclusions with convex right hand sides

Krystyna Grytczuk; Emilia Rotkiewicz

Annales Polonici Mathematici (1991)

  • Volume: 54, Issue: 1, page 13-19
  • ISSN: 0066-2216

Abstract

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 Abstract. The main result of the present paper deals with the existence of solutions of random functional-differential inclusions of the form ẋ(t, ω) ∈ G(t, ω, x(·, ω), ẋ(·, ω)) with G taking as its values nonempty compact and convex subsets of n-dimensional Euclidean space R n .

How to cite

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Krystyna Grytczuk, and Emilia Rotkiewicz. "Random differential inclusions with convex right hand sides." Annales Polonici Mathematici 54.1 (1991): 13-19. <http://eudml.org/doc/264115>.

@article{KrystynaGrytczuk1991,
abstract = { Abstract. The main result of the present paper deals with the existence of solutions of random functional-differential inclusions of the form ẋ(t, ω) ∈ G(t, ω, x(·, ω), ẋ(·, ω)) with G taking as its values nonempty compact and convex subsets of n-dimensional Euclidean space $R^n$.},
author = {Krystyna Grytczuk, Emilia Rotkiewicz},
journal = {Annales Polonici Mathematici},
keywords = {initial value problem; functional-differential inclusion; existence of random solutions; random fixed point theorem},
language = {eng},
number = {1},
pages = {13-19},
title = {Random differential inclusions with convex right hand sides},
url = {http://eudml.org/doc/264115},
volume = {54},
year = {1991},
}

TY - JOUR
AU - Krystyna Grytczuk
AU - Emilia Rotkiewicz
TI - Random differential inclusions with convex right hand sides
JO - Annales Polonici Mathematici
PY - 1991
VL - 54
IS - 1
SP - 13
EP - 19
AB -  Abstract. The main result of the present paper deals with the existence of solutions of random functional-differential inclusions of the form ẋ(t, ω) ∈ G(t, ω, x(·, ω), ẋ(·, ω)) with G taking as its values nonempty compact and convex subsets of n-dimensional Euclidean space $R^n$.
LA - eng
KW - initial value problem; functional-differential inclusion; existence of random solutions; random fixed point theorem
UR - http://eudml.org/doc/264115
ER -

References

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  1. [1] R. J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1-12. Zbl0163.06301
  2. [2] N. Dunford and J. T. Schwartz, Linear Operators I, Interscience Publ., New York 1967. Zbl0084.10402
  3. [3] C. J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), 53-72. Zbl0296.28003
  4. [4] M. Kisielewicz, Subtrajectory integrals of set-valued functions and neutral functional-differential inclusions, Funkcial. Ekvac. 32 (1989), 123-149. 
  5. [5] M. Kisielewicz, Differential Inclusions and Optimal Control, PWN and D. Reidel, Warszawa 1989 (in press). 
  6. [6] E. Michael, Continuous selections. I, Ann. of Math. 63 (1956), 361-382. Zbl0071.15902
  7. [7] A. Nowak, Applications of random fixed point theorems In the theory of generalized random Zbl0617.60059
  8. differential equations, Bull. Polish Acad. Sci. Math. 34 (7-8) (1986), 487-494. 
  9. [8] L. Rybiński, Multivalued contraction mappings with parameters and random fixed point theorems, Discuss. Math. 8 (1986), 101-108. Zbl0643.47052

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