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 LINEAR DIFFERENTIAL EQUATION WITH ADDITIONAL CONDITIONS AND FORMULAE FOR GREEN'S FUNCTION

2011 ◽  
Vol 16 (3) ◽  
pp. 401-417 ◽  
Author(s):  
Svetlana Roman
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence Condition ◽  
Linear Ordinary Differential Equation ◽  
Linearly Independent ◽  
Linear Differential

In this paper, we investigate the m-order linear ordinary differential equation with m linearly independent additional conditions. We have found the solution to this problem and give the formula and the existence condition of Green's function. We compare two Green's functions for two such problems with different additional conditions and apply these results to the problems with nonlocal boundary conditions.

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 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.

scholarly journals Generalized Green’s functions for second-order discrete boundary-value problems with nonlocal boundary conditions

2012 ◽  
Vol 53 ◽  
pp. 96-101 ◽  
Author(s):  
Gailė Paukštaitė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Conditions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence Condition ◽  
Second Order ◽  
Linear Functionals ◽  
Discrete Green’S Function ◽  
Sufficient Existence Condition

In this paper, generalized Green’s functions for second-order discrete boundaryvalueproblems with nonlocal boundary conditions are investigated, where the necessaryand sufficient existence condition of discrete Green’s function is not satisfied and nonlocalboundary conditions are described by linear functionals.

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

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