International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 375634, 18 pages
Research Article

Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach

1Naval Academy of Greece, 45110 Piraeus, Greece
2Technological Educational Institute of Piraeus, Department of Electronic Computer Systems, P.Ralli and Thivon 250, 12240 Athens, Greece

Received 9 April 2012; Revised 26 May 2012; Accepted 10 June 2012

Academic Editor: Michael Tom

Copyright © 2012 Panos K. Palamides and Alex P. Palamides. 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.


We investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a (positive) Green's function, the obtained solution is still of definite sign. Furthermore, we prove the existence of an entire continuum of solutions. Our technique relies on the continuum property (connectedness and compactness) of the solutions funnel (Kneser's Theorem), combined with the corresponding vector field.