Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 53, pp. 1-12.

Title: Existence of positive solutions and  eigenvalues intervals
       for nonlinear Sturm Liouville  problems  with a singular interface

Authors: Dasu Krishna Kiran Vamsi (Sri Sathya Sai Inst. of Higher Learning, India) 
Pallav Kumar Baruah (Sri Sathya Sai Inst. of Higher Learning, India)

Abstract: 
 In this article, we define the Green's matrix for a nonlinear Sturm Liouville problem
 associated with a pair of dynamic equations on time scales with a singularity at
 the point of interface. Then using iterative techniques, we obtain eigenvalue
 intervals for which there exist positive solutions. Then we present iterative schemes
 for approximating the solutions, and discus an  example that illustrates the
 the results obtained.

Submitted February 1, 2012. Published March 30, 2012.
Math Subject Classifications: 34B09, 34B27, 34L15, 47J25.
Key Words: Regular problems; singular problems; singular interface problems;
           time scale; dynamic equation; Green's matrix.