scholarly journals A STRONGLY ILL-POSED INTEGRO-DIFFERENTIAL PARABOLIC PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

2013 ◽  
Vol 18 (3) ◽  
pp. 395-414
Author(s):  
Alfredo Lorenzi
Keyword(s):  
Parabolic Problem ◽  
Dirichlet Boundary ◽  
Integral Boundary Conditions ◽  
Integral Condition ◽  
Normal Derivative ◽  
Integral Boundary ◽  
Additional Information ◽  
Ill Posed ◽  
Linear Integral ◽  
Continuous Dependence Results

Via Carleman estimates we prove uniqueness and continuous dependence results for an identification and strongly ill-posed linear integro-differential parabolic problem with the Dirichlet boundary condition, but with no initial condition. The additional information consists in a boundary linear integral condition involving the normal derivative of the temperature on the whole of the lateral boundary of the space-time domain.

scholarly journals Nontrivial Solutions for a System of Fractional q-Difference Equations Involving q-Integral Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 828 ◽  
Author(s):  
Yaohong Li ◽  
Jie Liu ◽  
Donal O’Regan ◽  
Jiafa Xu
Keyword(s):  
Boundary Conditions ◽  
Difference Equations ◽  
Integral Boundary Conditions ◽  
Integral Operators ◽  
First Eigenvalue ◽  
Nontrivial Solutions ◽  
Integral Boundary ◽  
The First Eigenvalue ◽  
Linear Integral ◽  
Linear Integral Operators

In this paper, we study the existence of nontrivial solutions for a system of fractional q-difference equations involving q-integral boundary conditions, and we use the topological degree to establish our main results by considering the first eigenvalue of some associated linear integral operators.

scholarly journals Existence of solution for 2-D time-fractional differential equations with a boundary integral condition

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Lotfi Kasmi ◽  
Amara Guerfi ◽  
Said Mesloub
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Integral Condition ◽  
Existence Of Solution ◽  
Boundary Integral ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Time Fractional Differential Equations ◽  
Uniqueness Of A Solution

AbstractIn this article, we prove the existence and uniqueness of a solution for 2-dimensional time-fractional differential equations with classical and integral boundary conditions. We start by writing this problem in the operator form and we choose suitable spaces and norms. Then we establish prior estimates from which we deduce the uniqueness of the strong solution. For the existence of solution for the fractional problem, we prove that the range of the operator generated by the considered problem is dense.

scholarly journals A three-point boundary value problem with an integral condition for a third-order partial differential equation

2005 ◽  
Vol 2005 (1) ◽  
pp. 33-43 ◽  
Author(s):  
C. Latrous ◽  
A. Memou
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Integral Condition ◽  
Order Equation ◽  
Order Partial Differential Equation ◽  
Point Boundary ◽  
Third Order ◽  
Integral Boundary

We prove the existence and uniqueness of a strong solution for a linear third-order equation with integral boundary conditions. The proof uses energy inequalities and the density of the range of the operator generated.

scholarly journals Further results on the investigation of solutions of integral boundary value problems

2015 ◽  
Vol 63 (1) ◽  
pp. 247-267 ◽  
Author(s):  
Miklós Rontó ◽  
Yana Varha ◽  
Kateryna Marynets
Keyword(s):  
Boundary Value ◽  
Autonomous Systems ◽  
Integral Boundary Conditions ◽  
Approximate Solutions ◽  
Integral Boundary ◽  
New Approach ◽  
Integral Boundary Value Problem ◽  
Suggested Technique ◽  
Integral Boundary Value Problems ◽  
Linear Integral

Abstract We give a new approach for the investigation of existence and construction of an approximate solutions of nonlinear non-autonomous systems of ordinary differential equations under nonlinear integral boundary conditions depending on the derivative. The constructivity of a suggested technique is shown on the example of non-linear integral boundary value problem with two solutions.

scholarly journals Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 174
Author(s):  
Chanakarn Kiataramkul ◽  
Weera Yukunthorn ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Banach Contraction Mapping Principle

In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

scholarly journals Non-Linear First-Order Differential Boundary Problems with Multipoint and Integral Conditions

2021 ◽  
Vol 5 (1) ◽  
pp. 15
Author(s):  
Misir J. Mardanov ◽  
Yagub A. Sharifov ◽  
Yusif S. Gasimov ◽  
Carlo Cattani
Keyword(s):  
Integral Equation ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Boundary Problems ◽  
Integral Boundary ◽  
Multipoint Problem ◽  
First Order ◽  
Banach Contraction ◽  
First Time ◽  
Banach Contraction Mapping Principle

This paper considers boundary value problem (BVP) for nonlinear first-order differential problems with multipoint and integral boundary conditions. A suitable Green function was constructed for the first time in order to reduce this problem into a corresponding integral equation. So that by using the Banach contraction mapping principle (BCMP) and Schaefer’s fixed point theorem (SFPT) on the integral equation, we can show that the solution of the multipoint problem exists and it is unique.

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