Electron. J. Diff. Eqns., Vol. 2005(2005), No. 28, pp. 1-12.

A new Green function concept for fourth-order differential equations

Kamil Orucoglu

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.

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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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