Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 47, pp. 1-15.

Title: Another understanding of fourth-order four-point 
       boundary-value problems
 
Authors: Petio Kelevedjiev  (Technical Univ. of Sliven, Sliven, Bulgaria)
         Panos K. Palamides (Naval Academy of Greece, Greece)
	 Nedyu Popivanov    (Univ. of Sofia 5, Bulgaria)

Abstract: 
 In this article we investigate the existence of positive and/or negative
 solutions of a classes of four-point boundary-value problems for
 fourth-order ordinary differential equations. The assumptions in this
 article are more relaxed than the known assumptions. Our technique relies on
 the continuum property (connectedness and compactness) of the solutions
 funnel (Knesser's Theorem), combined with the corresponding vector field's
 ones. This approach permits the extension of results (getting positive
 solutions) to nonlinear boundary conditions, whenever the corresponding
 Green's kernel is not of definite sign or there does not exist (see the last
 Corollary).
 
Submitted February 5, 2008. Published March 30, 2008.
Math Subject Classifications: 34B15, 34B25.
Key Words: Multipoint boundary value problem; positive solution; 
           vector field; third order differential equation; 
	   Green function; Krasnoselskii's fixed point theorem.