Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 121, pp. 1-12.
Title: Green's functional for second-order linear differential equation with
nonlocal conditions
Authors: Kamil Orucoglu (Istanbul Technical Univ., Turkey)
Kemal Ozen (Istanbul Technical Univ., Turkey)
Abstract:
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.
Submitted February 23, 2012. Published July 19, 2012.
Math Subject Classifications: 34A30, 34B05, 34B10, 34B27, 45A05.
Key Words: Green's function; nonlocal boundary conditions;
nonsmooth coefficient; adjoint problem.