Global Existence and Uniqueness for Abstract Evolutionary Differential Equations

2017 ◽  
pp. 245-255
Author(s):  
Yuming Qin
Keyword(s):  
Global Existence ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Global Existence And Uniqueness

scholarly journals Asymptotic Separation of Solutions to Fractional Stochastic Multi-Term Differential Equations

2021 ◽  
Vol 5 (4) ◽  
pp. 256
Author(s):  
Arzu Ahmadova ◽  
Nazim I. Mahmudov
Keyword(s):  
Global Existence ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
General Condition ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Asymptotic Results ◽  
Separation Rate ◽  
Global Existence And Uniqueness ◽  
Asymptotic Separation

In this paper, we study the exact asymptotic separation rate of two distinct solutions of Caputo stochastic multi-term differential equations (Caputo SMTDEs). Our goal in this paper is to establish results of the global existence and uniqueness and continuity dependence of the initial values of the solutions to Caputo SMTDEs with non-permutable matrices of order α∈(12,1) and β∈(0,1) whose coefficients satisfy a standard Lipschitz condition. For this class of systems, we then show the asymptotic separation property between two different solutions of Caputo SMTDEs with a more general condition based on λ. Furthermore, the asymptotic separation rate for the two distinct mild solutions reveals that our asymptotic results are general.

A Global Existence and Uniqueness Theorem for Ordinary Differential Equations

1976 ◽  
Vol 19 (1) ◽  
pp. 105-107 ◽  
Author(s):  
W. Derrick ◽  
L. Janos
Keyword(s):  
Global Existence ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Contraction Principle ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of Solutions ◽  
Banach Contraction ◽  
Global Existence And Uniqueness ◽  
The Banach Contraction Principle

As observed by A. Bielecki and others ([1], [3]) the Banach contraction principle, when applied to the theory of differential equations, provides proofs of existence and uniqueness of solutions only in a local sense. S. C. Chu and J. B. Diaz ([2]) have found that the contraction principle can be applied to operator or functional equations and even partial differential equations if the metric of the underlying function space is suitably changed.

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