A novel approach to construct the adjoint problem for a first-order functional integro-differential equation with general nonlocal condition
Yükleniyor...
Dosyalar
Tarih
2014
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In 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.
Açıklama
Anahtar Kelimeler
Green's function, functional integro-differential equation, nonsmooth coefficient, nonlocal condition, adjoint problem, Boundary-Value-Problems, Differential-Equations, Greens-Function, Existence
Kaynak
Lithuanian Mathematical Journal
WoS Q Değeri
Q2
Scopus Q Değeri
Q3
Cilt
54
Sayı
4
