Department of Mathematics
Faculty of Arts and Sciences
Yuzuncu Yil University
65000 Van, Turkey
email: alisirma01@gmail.com
Ali Sirma
Abstract:
In this work, we generalize so called Green's functional concept in
literature to second-order linear integro-differential equation with
nonlocal conditions. According to this technique, a linear completely
nonhomogeneous nonlocal problem for a second-order integro-differential
equation is reduced to one and one integral equation to identify
the Green's solution. The coefficients of the equation are assumed to be
generally nonsmooth functions satisfying some general properties such as
p-integrability and boundedness. We obtain new adjoint system and Green's
functional for second-order linear integro-differential equation with nonlocal
conditions. An application illustrate the adjoint system and the Green's
functional. Another application shows when the Green's functional
does not exist.
Submitted February 12, 2015. Published July 2, 2015.
Math Subject Classifications: 35A24, 65N80, 34B27.
Key Words: Adjoint system; Green's functional; p-integrability,
nonlocal boundary conditions.
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Ali Sirma Department of Mathematics Faculty of Arts and Sciences Yuzuncu Yil University 65000 Van, Turkey email: alisirma01@gmail.com |
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