A novel approach to construct the adjoint problem for a first-order functional integro-differential equation with general nonlocal condition

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dc.authorid0000-0002-8848-0058
dc.authorscopusid54403532200
dc.authorscopusid6506228517
dc.authorwosidOruçoğlu, Kamil/ABH-4956-2020
dc.contributor.authorÖzen, Kemal
dc.contributor.authorOruçoğlu, Kamil
dc.date.accessioned2022-05-11T14:31:14Z
dc.date.available2022-05-11T14:31:14Z
dc.date.issued2014
dc.departmentFakülteler, Fen Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractIn this work, with the aim of determining Green's solution or generalized Green's solution, we propose a novel constructive approach by which a linear or specific nonlinear problem involving general linear nonlocal condition for a first-order functional ordinary integro-differential equation with general nonsmooth coefficients satisfying some general properties such as p-integrability and boundedness is reduced to an integral equation. A system of two integro-algebraic equations, called the adjoint system, is constructed for this problem. Green's functional for the problem with trivial kernel and generalized Green's functional for the problem with nontrivial kernel are the unique solutions to the specific cases of this adjoint system. Green's functional and generalized Green's functional have two components. Their first components correspond to Green's function and generalized Green's function for the problem, respectively. Some illustrative applications are provided with known and unknown results.
dc.identifier.doi10.1007/s10986-014-9259-3
dc.identifier.endpage502
dc.identifier.issn0363-1672
dc.identifier.issn1573-8825
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-84939955271
dc.identifier.scopusqualityQ3
dc.identifier.startpage482
dc.identifier.urihttps://doi.org/10.1007/s10986-014-9259-3
dc.identifier.urihttps://hdl.handle.net/20.500.11776/7374
dc.identifier.volume54
dc.identifier.wosWOS:000346660700010
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorÖzen, Kemal
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofLithuanian Mathematical Journal
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectGreen's function
dc.subjectfunctional integro-differential equation
dc.subjectnonsmooth coefficient
dc.subjectnonlocal condition
dc.subjectadjoint problem
dc.subjectBoundary-Value-Problems
dc.subjectDifferential-Equations
dc.subjectGreens-Function
dc.subjectExistence
dc.titleA novel approach to construct the adjoint problem for a first-order functional integro-differential equation with general nonlocal condition
dc.typeArticle

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