scholarly journals On a Boundary Value Problem of Hybrid Functional Differential Inclusion with Nonlocal Integral Condition

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2667
Author(s):  
Ahmed M. A. El-Sayed ◽  
Wagdy G. El-Sayed ◽  
Somyya S. Amrajaa
Keyword(s):  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Nonlocal Condition ◽  
Boundary Value ◽  
Integral Condition ◽  
Hybrid Functional ◽  
Functional Differential Inclusion ◽  
Uniqueness Of The Solution ◽  
Nonlocal Integral Condition ◽  
Functional Differential

In this work, we present a boundary value problem of hybrid functional differential inclusion with nonlocal condition. The boundary conditions of integral and infinite points will be deduced. The existence of solutions and its maximal and minimal will be proved. A sufficient condition for uniqueness of the solution is given. The continuous dependence of the unique solution will be studied.

On a Nonlocal Boundary-value Problem for Two-dimensional Elliptic Equation

2001 ◽  
Vol 3 (1) ◽  
pp. 62-71
Author(s):  
Givi Berikelashvili ◽  
Nikolai I. Ionkin ◽  
Valentina A. Morozova
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Weighted Sobolev Space ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Two Dimensional ◽  
Averaging Operators ◽  
Nonlocal Integral Condition ◽  
Constant Coefficients

AbstractA boundary-value problem with a nonlocal integral condition is considered for a two-dimensional elliptic equation with constant coefficients and a mixed derivative. The existence and uniqueness of a weak solution of this problem are proved in a weighted Sobolev space. A difference scheme is constructed using the Steklov averaging operators.

scholarly journals INITIAL-BOUNDARY VALUE PROBLEM FOR ONE-DIMENSION HYPERBOLIC EQUATION WITH INTEGRAL BOUNDARY CONDITION

2017 ◽  
Vol 17 (8) ◽  
pp. 95-101
Author(s):  
M.V. Strigun
Keyword(s):  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Boundary Value ◽  
Integral Condition ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Generalized Solution ◽  
Integral Boundary ◽  
Nonlocal Integral Condition ◽  
Initial Boundary Value

In this paper, we study an initial-boundary value problem with nonlocal integral condition for a hyperbolic equation. The existence and uniqueness of a generalized solution of the problem is proved.

scholarly journals Inner boundary value problem with an integral condition for fractional diffusion equation

2021 ◽  
pp. 24-29
Author(s):  
Ф.М. Лосанова
Keyword(s):  
Diffusion Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Integral Condition ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Integral Conditions ◽  
Interior Boundary ◽  
Uniqueness Of The Solution ◽  
Fractional Differentiation Operator

В данной работе рассматривается нелокальная внутреннекраевая задача для уравнения дробной диффузии с оператором дробного дифференцирования в смысле Римана-Лиувилля с интегральными условиями. Исследуемая задача эквиваленто сведена к системе двух интегральных уравнений Вольтерра второго рода. Доказана теорема существования и единственности решения поставленной задачи. In this paper, we consider a nonlocal interior boundary value problem for the fractional diffusion equation with a fractional differentiation operator in the sense of Riemann-Liouville with integral conditions. The problem under study is equivalently reduced to a system of two Volterra integral equations of the second kind. The theorem of existence and uniqueness of the solution of the posed problem is proved.

scholarly journals On a Neutral Itô and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal Condition

2021 ◽  
Vol 5 (4) ◽  
pp. 201
Author(s):  
Ahmed M. A. El-Sayed ◽  
Hoda A. Fouad
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Continuous Dependence ◽  
Existence Of Solutions ◽  
Nonlocal Condition ◽  
Sufficient Conditions ◽  
Integral Condition ◽  
Uniqueness Of The Solution ◽  
Nonlocal Integral Condition ◽  
Fractional Orders

In this paper, we are concerned with the combinations of the stochastic Itô-differential and the arbitrary (fractional) orders derivatives in a neutral differential equation with a stochastic, nonlinear, nonlocal integral condition. The existence of solutions will be proved. The sufficient conditions for the uniqueness of the solution will be given. The continuous dependence of the unique solution will be studied.

scholarly journals Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
E. M. Hamdallah ◽  
Kh. W. El-kadeky
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Functional Differential Equation ◽  
Nonlocal Condition ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Second Order ◽  
Nonlocal Boundary Value Problem ◽  
Functional Differential

We study the existence of at least one monotonic positive solution for the nonlocal boundary value problem of the second-order functional differential equationx′′(t)=f(t,x(ϕ(t))),t∈(0,1), with the nonlocal condition∑k=1makx(τk)=x0,x′(0)+∑j=1nbjx′(ηj)=x1, whereτk∈(a,d)⊂(0,1),ηj∈(c,e)⊂(0,1), andx0,x1>0. As an application the integral and the nonlocal conditions∫adx(t)dt=x0,x′(0)+x(e)-x(c)=x1will be considered.

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