Green's functional for second-order linear differential equation with nonlocal conditions
In this work, we present a new constructive technique which is based on Green's functional concept. According to this technique, a linear completely nonhomogeneous nonlocal problem for a second-order ordinary differential equation is reduced to one and only one integral equation in order to...
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Texas State University
2012-07-01
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doaj-e1155cb73f954ffbb209f17bf7d605462020-11-24T23:35:48ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-07-012012121,112Green's functional for second-order linear differential equation with nonlocal conditionsKamil OrucogluKemal OzenIn this work, we present a new constructive technique which is based on Green's functional concept. According to this technique, a linear completely nonhomogeneous nonlocal problem for a second-order ordinary differential equation is reduced to one and only one integral equation in order to identify the Green's solution. The coefficients of the equation are assumed to be generally variable nonsmooth functions satisfying some general properties such as p-integrability and boundedness. A system of three integro-algebraic equations called the special adjoint system is obtained for this problem. A solution of this special adjoint system is Green's functional which enables us to determine the Green's function and the Green's solution for the problem. Some illustrative applications and comparisons are provided with some known results. http://ejde.math.txstate.edu/Volumes/2012/121/abstr.htmlGreen's functionnonlocal boundary conditionsnonsmooth coefficientadjoint problem |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Kamil Orucoglu Kemal Ozen |
spellingShingle |
Kamil Orucoglu Kemal Ozen Green's functional for second-order linear differential equation with nonlocal conditions Electronic Journal of Differential Equations Green's function nonlocal boundary conditions nonsmooth coefficient adjoint problem |
author_facet |
Kamil Orucoglu Kemal Ozen |
author_sort |
Kamil Orucoglu |
title |
Green's functional for second-order linear differential equation with nonlocal conditions |
title_short |
Green's functional for second-order linear differential equation with nonlocal conditions |
title_full |
Green's functional for second-order linear differential equation with nonlocal conditions |
title_fullStr |
Green's functional for second-order linear differential equation with nonlocal conditions |
title_full_unstemmed |
Green's functional for second-order linear differential equation with nonlocal conditions |
title_sort |
green's functional for second-order linear differential equation with nonlocal conditions |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
2012-07-01 |
description |
In this work, we present a new constructive technique which is based on Green's functional concept. According to this technique, a linear completely nonhomogeneous nonlocal problem for a second-order ordinary differential equation is reduced to one and only one integral equation in order to identify the Green's solution. The coefficients of the equation are assumed to be generally variable nonsmooth functions satisfying some general properties such as p-integrability and boundedness. A system of three integro-algebraic equations called the special adjoint system is obtained for this problem. A solution of this special adjoint system is Green's functional which enables us to determine the Green's function and the Green's solution for the problem. Some illustrative applications and comparisons are provided with some known results. |
topic |
Green's function nonlocal boundary conditions nonsmooth coefficient adjoint problem |
url |
http://ejde.math.txstate.edu/Volumes/2012/121/abstr.html |
work_keys_str_mv |
AT kamilorucoglu greensfunctionalforsecondorderlineardifferentialequationwithnonlocalconditions AT kemalozen greensfunctionalforsecondorderlineardifferentialequationwithnonlocalconditions |
_version_ |
1725524704432750592 |