Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 28, pp. 1-12.
Title: A new Green function concept for fourth-order
differential equations
Author: Kamil Orucoglu (Istanbul Technical Univ., Turkey)
Abstract:
A linear completely nonhomogeneous generally nonlocal multipoint
problem is investigated for a fourth-order differential equation
with generally nonsmooth coefficients satisfying some general
conditions such as p-integrability and boundedness. A system of
five integro-algebraic 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 Green-type 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.