scholarly journals On a boundary value problem of arbitrary orders differential inclusion with nonlocal, integral and infinite points boundary conditions

2021 ◽  
Vol 7 (3) ◽  
pp. 3896-3911
Author(s):  
A. M. A. El-Sayed ◽  
◽  
W. G. El-Sayed ◽  
Somyya S. Amrajaa ◽  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Differential Inclusion ◽  
Continuous Dependence ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Existence Results ◽  
Sufficient Condition ◽  
Nonlocal Boundary Value Problem ◽  
Fractional Orders

<abstract><p>In this work, we are concerned with a boundary value problem of fractional orders differential inclusion with nonlocal, integral and infinite points boundary conditions. We prove some existence results for that nonlocal boundary value problem. Next, the existence of maximal and minimal solutions is proved. Finally, the sufficient condition for the uniqueness and continuous dependence of solution are studied.</p></abstract>

Existence results for a second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 53 (1) ◽  
pp. 42-52
Author(s):  
Katarzyna Szymańska-Dȩbowska
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Existence Results ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

The paper focuses on existence of solutions of a system of nonlocal resonant boundary value problems , where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation. Imposing on the function f the following condition: the limit limλ→∞f(t, λ a) exists uniformly in a ∈ Sk−1, we have shown that the problem has at least one solution.

scholarly journals Constructing a basis from systems of eigenfunctions of one not strengthened regular boundary value problem

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 981-987 ◽  
Author(s):  
Makhmud Sadybekov ◽  
Gulnara Dildabek ◽  
Aizhan Tengayeva
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Fourier Method ◽  
Regular Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Variable Separation ◽  
Stationary Diffusion ◽  
New System

We investigate a nonlocal boundary value spectral problem for an ordinary differential equation in an interval. Such problems arise in solving the nonlocal boundary value problem for partial equations by the Fourier method of variable separation. For example, they arise in solving nonstationary problems of diffusion with boundary conditions of Samarskii-Ionkin type. Or they arise in solving problems with stationary diffusion with opposite flows on a part of the interval. The boundary conditions of this problem are regular but not strengthened regular. The principal difference of this problem is: the system of eigenfunctions is comlplete but not forming a basis. Therefore the direct applying of the Fourier method is impossible. Based on these eigenfunctions there is constructed a special system of functions that already forms the basis. However the obtained system is not already the system of the eigenfunctions of the problem. We demonstrate how this new system of functions can be used for solving a nonlocal boundary value problem on the example of the Laplace equation.

scholarly journals Investigation of matrix nullity for the second order discrete nonlocal boundary value problem

2013 ◽  
Vol 54 ◽  
pp. 49-54
Author(s):  
Gailė Paukštaitė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Second Order ◽  
Nonlocal Boundary Value Problem ◽  
Discrete Boundary Value Problem ◽  
The Matrix

In this paper we investigate the relation between the matrix nullity of the second order discrete boundary value problem and nonlocal boundary conditions. The obtained classification and examples are also presented.

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