A Strong Solution of an Evolution Problem with Integral Conditions

2002 ◽  
Vol 9 (1) ◽  
pp. 149-159
Author(s):  
S. Mesloub ◽  
A. Bouziani ◽  
N. Kechkar
Keyword(s):  
Functional Analysis ◽  
Parabolic Equation ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Energy Inequality ◽  
Integral Boundary Conditions ◽  
Analysis Method ◽  
Integral Conditions ◽  
Integral Boundary ◽  
Singular Parabolic Equation

Abstract The paper is devoted to proving the existence and uniqueness of a strong solution of a mixed problem with integral boundary conditions for a certain singular parabolic equation. A functional analysis method is used. The proof is based on an energy inequality and on the density of the range of the operator generated by the studied problem.

scholarly journals Boundary value problem with integral conditions for a linear third-order equation

2003 ◽  
Vol 2003 (11) ◽  
pp. 553-567 ◽  
Author(s):  
M. Denche ◽  
A. Memou
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Order Equation ◽  
Integral Conditions ◽  
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 generated operator.

scholarly journals Boundary Value Problems for Fractional Differential Equations with Fractional Multiterm Integral Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Arisa Singubol
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Conditions ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Fractional Differential

We discuss the existence and uniqueness of solutions for boundary value problems involving multiterm fractional integral boundary conditions. Our study relies on standard fixed point theorems. Illustrative examples are also presented.

scholarly journals Mixed problem with boundary integral conditions for a certain parabolic equation

1996 ◽  
Vol 9 (3) ◽  
pp. 323-330 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Parabolic Equation ◽  
Present Article ◽  
Mixed Problem ◽  
Existence And Uniqueness ◽  
Energy Inequality ◽  
Boundary Integral ◽  
Integral Conditions ◽  
Uniqueness Of A Solution

The present article is devoted to a proof of the existence and uniqueness of a solution of a mixed problem with boundary integral conditions for a certain parabolic equation. The proof is based on an energy inequality and on the fact that the range of the operator generated by the problem is dense.

scholarly journals Existence results for coupled differential equations of non-integer order with Riemann-Liouville, Erdélyi-Kober integral conditions

2021 ◽  
Vol 6 (12) ◽  
pp. 13004-13023
Author(s):  
Dumitru Baleanu ◽  
◽  
S. Hemalatha ◽  
P. Duraisamy ◽  
P. Pandiyan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Integral Conditions ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Uniqueness Of A Solution

<abstract><p>This paper proposes the existence and uniqueness of a solution for a coupled system that has fractional differential equations through Erdélyi-Kober and Riemann-Liouville fractional integral boundary conditions. The existence of the solution for the coupled system by adopting the Leray-Schauder alternative. The uniqueness of solution for the problem can be found using Banach fixed point theorem. In order to verify the proposed criterion, some numerical examples are also discussed.</p></abstract>

scholarly journals Existence and Uniqueness Results for a Coupled System of Caputo-Hadamard Fractional Differential Equations with Nonlocal Hadamard Type Integral Boundary Conditions

2020 ◽  
Vol 4 (2) ◽  
pp. 13 ◽  
Author(s):  
Shorog Aljoudi ◽  
Bashir Ahmad ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we study a coupled system of Caputo-Hadamard type sequential fractional differential equations supplemented with nonlocal boundary conditions involving Hadamard fractional integrals. The sufficient criteria ensuring the existence and uniqueness of solutions for the given problem are obtained. We make use of the Leray-Schauder alternative and contraction mapping principle to derive the desired results. Illustrative examples for the main results are also presented.

scholarly journals Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Jian Chang ◽  
Jian-Ping Sun ◽  
Ya-Hong Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Integral Boundary Conditions ◽  
Multiple Positive Solutions ◽  
Stieltjes Integral ◽  
Integral Conditions ◽  
Third Order ◽  
Integral Boundary

We consider the following third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions:u′′′t+ft,uαt=0,  t∈0,1,  u0=γuη1+λ1uandu′′0=0,  u1=βuη2+λ2u, where0<η1<η2<1,0≤γ,β≤1,α:[0,1]→[0,1]is continuous,α(t)≥tfort∈[0,1], andα(t)≤η2fort∈[η1,η2]. Under some suitable conditions, by applying a fixed point theorem due to Avery and Peterson, we obtain the existence of multiple positive solutions to the above problem. An example is also included to illustrate the main results obtained.

scholarly journals Existence and Uniqueness Theorems for a Fractional Differential Equation with Impulsive Effect under Band-Like Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zihan Gao ◽  
Tianlin Hu ◽  
Huihui Pang
Keyword(s):  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Integral Boundary Conditions ◽  
Continuous Operator ◽  
Impulsive Effect ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Caputo Fractional Differential Equations ◽  
Multiple Band ◽  
Fractional Differential

In this paper, we consider a class of nonlinear Caputo fractional differential equations with impulsive effect under multiple band-like integral boundary conditions. By constructing an available completely continuous operator, we establish some criteria for judging the existence and uniqueness of solutions. Finally, an example is presented to demonstrate our main results.

Sign in / Sign up

Export Citation Format

Share Document