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Green and Generalized Green’s Functionals of Linear Local and Nonlocal Problems for Ordinary Integro-differential Equations

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Abstract

A linear, completely nonhomogeneous, generally nonlocal, multipoint problem is investigated for a second-order ordinary integro-differential equation with generally nonsmooth coefficients, satisfying some general conditions like p-integrability and boundedness. A system of three integro-algebraic equations named the adjoint system is introduced for the solution. The solvability conditions are found by the solutions of the homogeneous adjoint system in an “alternative theorem”. A version of a Green’s functional is introduced as a special solution of the adjoint system. For the problem with a nontrivial kernel also a notion of a generalized Green’s functional is introduced by a projection operator defined on the space of solutions. It is also shown that the classical Green and Cauchy type functions are special forms of the Green’s functional.

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Authors and Affiliations

  1. Faculty of Science, Istanbul Technical University, Maslak, 80626, Istanbul, Turkey

    Seyidali S. Akhiev

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  1. Seyidali S. Akhiev
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The author passed away in 2006 prior to publication of the article.

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Akhiev, S.S. Green and Generalized Green’s Functionals of Linear Local and Nonlocal Problems for Ordinary Integro-differential Equations. Acta Appl Math 95, 73–93 (2007). https://doi.org/10.1007/s10440-006-9056-z

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  • DOI: https://doi.org/10.1007/s10440-006-9056-z

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