On uniqueness of solutions to martingale problems — counterexamples and sufficient criteria

Abstract The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces.

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Existence and uniqueness of solutions for a class of abstract nonlinear wave equation

Proceedings of the seventh International Colloquium on Differential Equations ◽

10.1515/9783112319185-009 ◽

1997 ◽

pp. 57-66

Keyword(s):

Wave Equation ◽

Nonlinear Wave ◽

Nonlinear Wave Equation ◽

Existence And Uniqueness ◽

Uniqueness Of Solutions

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Existence and uniqueness of positive solutions for nonlinear fractional mixed problems

Georgian Mathematical Journal ◽

10.1515/gmj-2021-2102 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Alberto Cabada ◽

Om Kalthoum Wanassi

Keyword(s):

Existence And Uniqueness ◽

Fixed Point Theory ◽

Mixed Boundary ◽

Point Theory ◽

Uniqueness Of Solutions ◽

Nonlinear Part ◽

Banach Contraction ◽

Fractional Differential ◽

Exhaustive Study ◽

The Banach Contraction Principle

Abstract This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear Riemann–Liouville fractional differential equations with mixed boundary value conditions. An exhaustive study of the sign of the related Green’s function is carried out. Under suitable assumptions on the asymptotic behavior of the nonlinear part of the equation at zero and at infinity, and by application of the fixed point theory of compact operators defined in suitable cones, it is proved that there exists at least one solution of the considered problem. Moreover, the method of lower and upper solutions is developed and the existence of solutions is deduced by a combination of both techniques. In particular cases, the Banach contraction principle is used to ensure the uniqueness of solutions.

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Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives

Symmetry ◽

10.3390/sym13081431 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1431

Author(s):

Bilal Basti ◽

Nacereddine Hammami ◽

Imadeddine Berrabah ◽

Farid Nouioua ◽

Rabah Djemiat ◽

...

Keyword(s):

Mathematical Model ◽

Existence And Uniqueness ◽

Fractional Derivatives ◽

Fixed Point Theorems ◽

Existence Of Solutions ◽

Biological Models ◽

Uniqueness Of Solutions ◽

Caputo Fractional Derivatives ◽

Single Form ◽

Stability Results

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

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