Electron. J. Diff. Equ., Vol. 2012 (2012), No. 53, pp. 1-12.

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

D. K. K. Vamsi, Pallav Kumar Baruah

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.

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Pallav Kumar Baruah
Department of Mathematics and computer Science
Sri Sathya Sai Institute of Higher Learning
Prasanthi Nilayam, Puttaparthi
Ananthapur, Andhra-Pradesh, 515134, India
email: pkbaruah@sssihl.edu.in
Dasu Krishna Kiran Vamsi
Department of Mathematics and computer Science
Sri Sathya Sai Institute of Higher Learning
Prasanthi Nilayam, Puttaparthi
Ananthapur, Andhra-Pradesh, 515134, India
email: dkkvamsi@gmail.com

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