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International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 275-284
http://dx.doi.org/10.1155/S016117128800033X

Solvability of a fourth order boundary value problem with periodic boundary conditions

Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA

Received 28 May 1987; Revised 16 July 1987

Copyright © 1988 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary conditions.