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

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

<p/> <p>We investigate a second-order discrete problem with two additional conditions which are described by a pair of linearly independent linear functionals. We have found the solution to this problem and presented a formula and the existence condition of Green's function if the g...

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Main Authors: Roman Svetlana, &#352;tikonas Art&#363;ras
Format: Article
Language:English
Published: SpringerOpen 2011-01-01
Series:Boundary Value Problems
Online Access:http://www.boundaryvalueproblems.com/content/2011/767024
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spelling doaj-79f17977b56547b890e0555ef06a24072020-11-24T21:52:53ZengSpringerOpenBoundary Value Problems1687-27621687-27702011-01-0120111767024Green's Function for Discrete Second-Order Problems with Nonlocal Boundary ConditionsRoman Svetlana&#352;tikonas Art&#363;ras<p/> <p>We investigate a second-order discrete problem with two additional conditions which are described by a pair of linearly independent linear functionals. We have found the solution to this problem and 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 nonhomogeneous 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 with nonlocal boundary conditions.</p>http://www.boundaryvalueproblems.com/content/2011/767024
collection DOAJ
language English
format Article
sources DOAJ
author Roman Svetlana
&#352;tikonas Art&#363;ras
spellingShingle Roman Svetlana
&#352;tikonas Art&#363;ras
Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions
Boundary Value Problems
author_facet Roman Svetlana
&#352;tikonas Art&#363;ras
author_sort Roman Svetlana
title Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions
title_short Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions
title_full Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions
title_fullStr Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions
title_full_unstemmed Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions
title_sort green's function for discrete second-order problems with nonlocal boundary conditions
publisher SpringerOpen
series Boundary Value Problems
issn 1687-2762
1687-2770
publishDate 2011-01-01
description <p/> <p>We investigate a second-order discrete problem with two additional conditions which are described by a pair of linearly independent linear functionals. We have found the solution to this problem and 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 nonhomogeneous 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 with nonlocal boundary conditions.</p>
url http://www.boundaryvalueproblems.com/content/2011/767024
work_keys_str_mv AT romansvetlana greensfunctionfordiscretesecondorderproblemswithnonlocalboundaryconditions
AT 352tikonasart363ras greensfunctionfordiscretesecondorderproblemswithnonlocalboundaryconditions
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