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.