scholarly journals Existence and Uniqueness Results for a Smooth Model of Periodic Infectious Diseases

2016 ◽  
Vol 2016 ◽  
pp. 1-4
Author(s):  
Guy Degla
Keyword(s):  
Integral Equation ◽  
Asymptotic Stability ◽  
Existence And Uniqueness ◽  
Bounded Solution ◽  
Stability Result ◽  
Implicit Function ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Small Delay ◽  
Smooth Model

We prove the existence of a curve (with respect to the scalar delay) of periodic positive solutions for a smooth model of Cooke-Kaplan’s integral equation by using the implicit function theorem under suitable conditions. We also show a situation in which any bounded solution with a sufficiently small delay is isolated, clearing an asymptotic stability result of Cooke and Kaplan.

scholarly journals Existence and Uniqueness of the Solution for an Integral Equation with Supremum, via w-Distances

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1554 ◽  
Author(s):  
Veronica Ilea ◽  
Diana Otrocol
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Stability Result ◽  
Fixed Point Problem ◽  
Comparison Theorems ◽  
Point Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Uniqueness Of The Solution

Following the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of an integral equation with supremum. The paper ends with the study of Gronwall-type theorems, comparison theorems and a result regarding a Ulam–Hyers stability result for the corresponding fixed point problem.

Existence and uniqueness results for a class of elliptic equations with exponential nonlinearity

2005 ◽  
Vol 135 (5) ◽  
pp. 959-983
Author(s):  
Kwangseok Choe
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Existence Results ◽  
Implicit Function ◽  
Exponential Nonlinearity ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Semilinear Elliptic

We establish existence results for a class of semilinear elliptic equations with exponential nonlinearity by studying a suitable eigenvalue problem. We also establish a uniqueness result for those equations by making use of the implicit function theorem.

Existence and uniqueness results for a class of elliptic equations with exponential nonlinearity

2005 ◽  
Vol 135 (5) ◽  
pp. 959-983 ◽  
Author(s):  
Kwangseok Choe
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Existence Results ◽  
Implicit Function ◽  
Exponential Nonlinearity ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Semilinear Elliptic

We establish existence results for a class of semilinear elliptic equations with exponential nonlinearity by studying a suitable eigenvalue problem. We also establish a uniqueness result for those equations by making use of the implicit function theorem.

scholarly journals Decay result in a problem of a nonlinearly damped wave equation with variable exponent

2021 ◽  
Vol 7 (2) ◽  
pp. 3067-3082
Author(s):  
Mohammad Kafini ◽  
◽  
Jamilu Hashim Hassan ◽  
Mohammad M. Al-Gharabli ◽  
◽  
...  
Keyword(s):  
Wave Equation ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Galerkin Approximation ◽  
Stability Result ◽  
Time Dependent ◽  
Damped Wave Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Frictional Damping

<abstract><p>In this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy associated to the solution of the problem under consideration.</p></abstract>

scholarly journals On mathematical modelling of temporal spatial spread of epidemics

2020 ◽  
Vol 15 ◽  
pp. 6
Author(s):  
Kh.A. Khachatryan ◽  
A.Zh. Narimanyan ◽  
A.Kh. Khachatryan
Keyword(s):  
Integral Equation ◽  
Mathematical Modelling ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Spatial Spread ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Convergence Results ◽  
Integral Differential Equations ◽  
Multidimensional Integral

In the present work a generalized epidemic model containing a system of integral-differential equations is described. Using different transformations the system is reduced to a single nonlinear multidimensional integral equation. For the obtained equation the existence and uniqueness results are proved. Based on theoretical convergence results several application examples are presented with corresponding numerical results.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

scholarly journals BSDEs with polynomial growth generators

2000 ◽  
Vol 13 (3) ◽  
pp. 207-238 ◽  
Author(s):  
Philippe Briand ◽  
René Carmona
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Polynomial Growth ◽  
Probabilistic Representation ◽  
Existence And Uniqueness Results ◽  
State Variable ◽  
Cahn Equation ◽  
Uniqueness Results ◽  
Terminal Time

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

Nontrivial solutions of non-autonomous dirichlet fractional discrete problems

2020 ◽  
Vol 23 (4) ◽  
pp. 980-995
Author(s):  
Alberto Cabada ◽  
Nikolay Dimitrov
Keyword(s):  
Existence And Uniqueness ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Fractional Difference ◽  
Nonlinear Part ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Difference Equation ◽  
Discrete Problems ◽  
Series Of Functions

AbstractIn this paper, we introduce a two-point boundary value problem for a finite fractional difference equation with a perturbation term. By applying spectral theory, an associated Green’s function is constructed as a series of functions and some of its properties are obtained. Under suitable conditions on the nonlinear part of the equation, some existence and uniqueness results are deduced.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

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