Viability theory and fuzzy differential equations

Donal O'Regan

doi:10.1016/j.fss.2004.08.008

Viability theory and fuzzy differential equations

Donal O'Regan

Mathematics

Department of Mathematical Sciences

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

47 Citations (Scopus)

Abstract

New results are presented which guarantee the existence of viable solutions to differential inclusions. We show that a viable solution exists if (i) a tangency condition is satisfied, and (ii) there exists a maximal solution to an appropriate differential equation. In addition, we discuss the topological structure of the solution set. These results will then be used with the stacking theorem to establish new existence criteria for fuzzy differential equations if there exists a maximal solution for an appropriate set of differential equations. (c) 2004 Elsevier B.V. All rights reserved.

Original language	English (Ireland)
Pages (from-to)	563-580
Number of pages	18
Journal	Fuzzy Sets And Systems
Volume	151
Issue number	3
DOIs	https://doi.org/10.1016/j.fss.2004.08.008
Publication status	Published - 1 May 2005

Keywords

Differential inclusion
Maximal solution
Set
Stacking theorem
Viable solution

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Agarwal, RP,O'Regan, D,Lakshmikantham, V

Access to Document

10.1016/j.fss.2004.08.008

Cite this

@article{86ad8a6e7fed4f76bb32b45b692f3a1b,

title = "Viability theory and fuzzy differential equations",

abstract = "New results are presented which guarantee the existence of viable solutions to differential inclusions. We show that a viable solution exists if (i) a tangency condition is satisfied, and (ii) there exists a maximal solution to an appropriate differential equation. In addition, we discuss the topological structure of the solution set. These results will then be used with the stacking theorem to establish new existence criteria for fuzzy differential equations if there exists a maximal solution for an appropriate set of differential equations. (c) 2004 Elsevier B.V. All rights reserved.",

keywords = "Differential inclusion, Maximal solution, Set, Stacking theorem, Viable solution",

author = "Donal O'Regan",

year = "2005",

month = may,

day = "1",

doi = "10.1016/j.fss.2004.08.008",

language = "English (Ireland)",

volume = "151",

pages = "563--580",

journal = "Fuzzy Sets And Systems",

number = "3",

}

TY - JOUR

T1 - Viability theory and fuzzy differential equations

AU - O'Regan, Donal

PY - 2005/5/1

Y1 - 2005/5/1

N2 - New results are presented which guarantee the existence of viable solutions to differential inclusions. We show that a viable solution exists if (i) a tangency condition is satisfied, and (ii) there exists a maximal solution to an appropriate differential equation. In addition, we discuss the topological structure of the solution set. These results will then be used with the stacking theorem to establish new existence criteria for fuzzy differential equations if there exists a maximal solution for an appropriate set of differential equations. (c) 2004 Elsevier B.V. All rights reserved.

AB - New results are presented which guarantee the existence of viable solutions to differential inclusions. We show that a viable solution exists if (i) a tangency condition is satisfied, and (ii) there exists a maximal solution to an appropriate differential equation. In addition, we discuss the topological structure of the solution set. These results will then be used with the stacking theorem to establish new existence criteria for fuzzy differential equations if there exists a maximal solution for an appropriate set of differential equations. (c) 2004 Elsevier B.V. All rights reserved.

KW - Differential inclusion

KW - Maximal solution

KW - Set

KW - Stacking theorem

KW - Viable solution

UR - https://www.scopus.com/pages/publications/14544290543

U2 - 10.1016/j.fss.2004.08.008

DO - 10.1016/j.fss.2004.08.008

M3 - Article

VL - 151

SP - 563

EP - 580

JO - Fuzzy Sets And Systems

JF - Fuzzy Sets And Systems

IS - 3

ER -

Viability theory and fuzzy differential equations

Abstract

Keywords

Authors (Note for portal: view the doc link for the full list of authors)

Access to Document

Other files and links

Fingerprint

Cite this