Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 171, pp. 1-8.

Title: Positive solutions for singular  Sturm-Liouville boundary value
       problems on the half line

Authors: Jiafa Xu    (Qingdao Technological Univ., Shandong, China)
         Zhilin Yang (Qingdao Technological Univ., Shandong, China)

Abstract:
 This article concerns the existence and multiplicity of positive
 solutions for the singular Sturm-Liouville boundary value
 problem
 $$\displaylines{
 (p(t)u'(t))'+h(t)f(t,u(t))=0,\quad 0<t<\infty,\cr
 au(0)-b\lim_{t\to 0^+}p(t)u'(t)=0,\cr
 c\lim_{t\to \infty}u(t)+d\lim_{t\to \infty}p(t)u'(t)=0.
 }$$
 We use fixed point index theory to establish our main results based
 on a priori estimates derived by utilizing spectral properties  of
 associated linear integral operators.
 
Submitted April 1, 2010. Published November 30, 2010.
Math Subject Classifications: 34B40, 34B16, 47H07, 47H11, 45M20.
Key Words: Sturm-Liouville problem on the half line; positive solution; 
           fixed point index; spectral radius.