Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 08, pp. 1-19.

Title: A necessary and sufficient condition for the existence of
       positive solutions to singular boundary-value problems of 
       higher order differential equations
       
Authors: Chenglong Zhao (Shandong Normal Univ., Jinan, China)
         Yanyan Yuan  (Shandong Normal Univ., Jinan, China)
	 Yansheng Liu (Shandong Normal Univ., Jinan, China)

Abstract: 
 By constructing some special cones and using fixed point
 theorem of cone expansion and compression, this paper
 presents some necessary and sufficient conditions for
 the existence of  $C^{4n-2}$ positive solutions to a
 class of singular boundary-value problems.
 Some examples are presented to illustrate our main results.
 
Submitted September 8, 2005. Published January 19, 2006.
Math Subject Classifications: 34B16.
Key Words: Singular sublinear boundary-value problem; positive solution;
           fixed point theorem; cone; higher order differential equation.