Random coincidence degree theory with applications to random differential inclusions

Enayet U, Tarafdar; P. Watson; George Xian-Zhi Yuan

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 4, page 725-748
  • ISSN: 0010-2628

Abstract

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The aim of this paper is to establish a random coincidence degree theory. This degree theory possesses all the usual properties of the deterministic degree theory such as existence of solutions, excision and Borsuk’s odd mapping theorem. Our degree theory provides a method for proving the existence of random solutions of the equation L x ∈ N ( ω , x ) where L : dom L ⊂ X → Z is a linear Fredholm mapping of index zero and N : Ω × G ¯ → 2 Z is a noncompact Carathéodory mapping. Applications to random differential inclusions are also considered.

How to cite

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Tarafdar, Enayet U,, Watson, P., and Yuan, George Xian-Zhi. "Random coincidence degree theory with applications to random differential inclusions." Commentationes Mathematicae Universitatis Carolinae 37.4 (1996): 725-748. <http://eudml.org/doc/247880>.

@article{Tarafdar1996,
abstract = {The aim of this paper is to establish a random coincidence degree theory. This degree theory possesses all the usual properties of the deterministic degree theory such as existence of solutions, excision and Borsuk’s odd mapping theorem. Our degree theory provides a method for proving the existence of random solutions of the equation $Lx\in N(\omega ,x)$ where $L:\text\{\it dom\}\hspace\{1.3pt\}L\subset X\rightarrow Z$ is a linear Fredholm mapping of index zero and $N:\Omega \times \overline\{G\}\rightarrow 2^Z$ is a noncompact Carathéodory mapping. Applications to random differential inclusions are also considered.},
author = {Tarafdar, Enayet U,, Watson, P., Yuan, George Xian-Zhi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Carathéodory upper semicontinuous; random (stochastic) topological degree; Souslin family; measurable space; Carathéodory u.s.c. maps; random degree; Souslin family; measurable spaces},
language = {eng},
number = {4},
pages = {725-748},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Random coincidence degree theory with applications to random differential inclusions},
url = {http://eudml.org/doc/247880},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Tarafdar, Enayet U,
AU - Watson, P.
AU - Yuan, George Xian-Zhi
TI - Random coincidence degree theory with applications to random differential inclusions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 4
SP - 725
EP - 748
AB - The aim of this paper is to establish a random coincidence degree theory. This degree theory possesses all the usual properties of the deterministic degree theory such as existence of solutions, excision and Borsuk’s odd mapping theorem. Our degree theory provides a method for proving the existence of random solutions of the equation $Lx\in N(\omega ,x)$ where $L:\text{\it dom}\hspace{1.3pt}L\subset X\rightarrow Z$ is a linear Fredholm mapping of index zero and $N:\Omega \times \overline{G}\rightarrow 2^Z$ is a noncompact Carathéodory mapping. Applications to random differential inclusions are also considered.
LA - eng
KW - Carathéodory upper semicontinuous; random (stochastic) topological degree; Souslin family; measurable space; Carathéodory u.s.c. maps; random degree; Souslin family; measurable spaces
UR - http://eudml.org/doc/247880
ER -

References

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