scholarly journals Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-23 ◽  
Author(s):  
Svetlana Roman ◽  
Artūras Štikonas
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Second Order

scholarly journals Linear ODE with nonlocal boundary conditions and Green’s functions for such problems

2019 ◽  
Vol 51 ◽  
pp. 379-384
Author(s):  
Svetlana Roman ◽  
Artūras Štikonas
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Linear Ode

In this article we investigate a formula for the Green’s function for the n-orderlinear differential equation with n additional conditions. We use this formula for calculatingthe Green’s function for problems with nonlocal boundary conditions.

scholarly journals The properties of Green’s functions for one stationary problem with nonlocal boundary conditions

2019 ◽  
Vol 50 ◽  
Author(s):  
Svetlana Roman ◽  
Artūras Štikonas
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Stationary Problem

In this paper we research Green’s function properties for stationary problem with four-pointnonlocal boundary conditions. Dependence of these functions on values ξ and γ is investigated. Green’sfunctions graphs with various values ξ and γ are presented.

scholarly journals Green’s function for discrete problems with nonlocal boundary conditions

2011 ◽  
Vol 52 ◽  
pp. 291-296
Author(s):  
Svetlana Roman ◽  
Artūras Štikonas
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Homogeneous Equation ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence Condition ◽  
Discrete Problem ◽  
Discrete Problems ◽  
Inhomogeneous Problems

In this article, we investigate an m-order discrete problem with additional conditions which are described by m of linearly independent linear functionals. We have presented a formula and the existence condition of Green’s function, if the general solution of a homogeneous equation is known. We have obtained the relation between two Green’s functions of two inhomogeneous problems. It allows us to find Green’s function for the same equation but with different additional conditions. The obtained results are applied to problems withnonlocal boundary conditions. This research was funded by a grant (No. MIP-051/2011) from the Research Council of Lithuania

scholarly journals A Study of Caputo-Hadamard-Type Fractional Differential Equations with Nonlocal Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Wafa Shammakh
Keyword(s):  
Differential Equations ◽  
Green’S Function ◽  
Green's Function ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Nonlinear Boundary Value Problems ◽  
Uniqueness Results ◽  
Fractional Differential

Existence and uniqueness results of positive solutions to nonlinear boundary value problems for Caputo-Hadamard fractional differential equations by using some fixed point theorems are presented. The related Green’s function for the boundary value problem is given, and some useful properties of Green’s function are obtained. Example is presented to illustrate the main results.

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