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

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.

Keywords

• Regular problems
• singular problems
• singular interface problems
• time scale
• dynamic equation
• Green's matrix