scholarly journals A Global Existence and Uniqueness Result for Functional Integro-Differential Equations in Banach Spaces

2012 ◽  
Vol 58 (1) ◽  
Author(s):  
M. Benchohra ◽  
S. Litimein
Keyword(s):  
Global Existence ◽  
Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Global Existence And Uniqueness

SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE AND INVERSE PROBLEMS

2003 ◽  
Vol 13 (12) ◽  
pp. 1745-1766 ◽  
Author(s):  
A. FAVINI ◽  
A. LORENZI
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Parabolic Type ◽  
Initial Boundary ◽  
Uniqueness Result ◽  
Initial Boundary Value Problems ◽  
First Order ◽  
Global Existence And Uniqueness ◽  
End Use ◽  
Initial Boundary Value

We prove a global existence and uniqueness result for the recovery of unknown scalar kernels in linear singular first-order integro-differential initial-boundary value problems in Banach spaces. To this end use is made of suitable weighted Lp-spaces. Finally, we give a few applications to explicit singular partial integro-differential equations of parabolic type.

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.

Global existence and uniqueness result for the diffusive Peterlin viscoelastic model

2015 ◽  
Vol 120 ◽  
pp. 154-170 ◽  
Author(s):  
Mária Lukáčová - Medvid’ová ◽  
Hana Mizerová ◽  
Šárka Nečasová
Keyword(s):  
Global Existence ◽  
Existence And Uniqueness ◽  
Viscoelastic Model ◽  
Uniqueness Result ◽  
Global Existence And Uniqueness
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