Electron. J. Diff. Eqns., Vol. 2005(2005), No. 28, pp. 112.
A new Green function concept for fourthorder
differential equations
Kamil Orucoglu
Abstract:
A linear completely nonhomogeneous generally nonlocal multipoint
problem is investigated for a fourthorder differential equation
with generally nonsmooth coefficients satisfying some general
conditions such as pintegrability and boundedness. A system of
five integroalgebraic equations called an adjoint system is
introduced for this problem. A concept of a Green functional is
introduced as a special solution of the adjoint system. This new
type of Green function concept, which is more natural than the
classical Greentype function concept, and an integral form of the
nonhomogeneous problems can be found more naturally. Some
applications are given for elastic bending problems.
Submitted November 19, 2004. Published March 6, 2005.
Math Subject Classifications: 34A30, 34B05, 34B10, 34B27,
45A05, 45E35, 45J05.
Key Words: Green function; linear operator; multipoint;
nonlocal problem; nonsmooth coefficient; differential equation.
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Kamil Orucoglu
Istanbul Technical University
Faculty of Science, Maslak 34469
Istanbul, Turkey
email: koruc@itu.edu.tr 
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