Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 117, pp. 1-9.

Title: An application of a global bifurcation theorem to the existence
      of solutions for integral inclusions
  
Author: Stanislaw Domachowski (Univ. of Gdansk, Poland)
 
Abstract:
 We prove the existence of solutions to  Hammerstein integral
 inclusions of weakly  completely continuous type.
 As a consequence we obtain an existence theorem for
 differential inclusions, with Sturm-Liouville boundary
 conditions,
 $$\displaylines{
 u''(t) \in -F(t,u(t),u'(t)) \quad\hbox{for a.e. } t\in(a,b) \cr
 l(u) = 0.
 }$$
 
Submitted April 17, 2008. Published August 25, 2008.
Math Subject Classifications: 47H04, 34A60, 34B24.
Key Words: Integral inclusion; differential inclusion;
 global bifurcation; selectors; Sturm-Liouville boundary conditions.