Geodesic
A new Green function concept for fourth-order differential equations
Electronic journal of differential equations, Tome 2005 (2005)
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.
Classification : 34A30, 34B05, 34B10, 34B27, 45A05, 45E35, 45J05
Keywords: Green function, linear operator, multipoint, nonlocal problem, nonsmooth coefficient, differential equation 
@article{EJDE_2005__2005__a291,
     author = {Orucoglu,  Kamil},
     title = {A new {Green} function concept for fourth-order differential equations},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1076.34027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a291/}
}
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Orucoglu,  Kamil. A new Green function concept for fourth-order differential equations. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a291/