Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 254695, 23 pages
http://dx.doi.org/10.5402/2011/254695
Research Article

Disconjugacy and Nonoscillation Domains for Nonlinear Singular Interface Problems on Semi-Infinite Time Scales

Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, Prasanthi Nilayam, Ananthapur, Andhra Pradesh, Puttaparthi 515134, India

Received 18 July 2011; Accepted 6 September 2011

Academic Editors: A. Carpio and J.-F. Colombeau

Copyright Β© 2011 D. K. K. Vamsi and Pallav Kumar Baruah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We define and discuss the disconjugacy (π’Ÿ) and nonoscillation (𝒩) domains for a pair of dynamic equations along with matching interface conditions on the semi-infinite time scale [0,𝑐]𝕋βˆͺ[𝜎(𝑐),∞]𝕋. We show that these domains are closed and convex subsets of the parameter space ℝ𝑛+π‘š. The theory developed is used to discuss the oscillatory behavior of initial and boundary value problems associated with interface problems in the fields of applied elasticity, acoustic wave guides in ocean, and transverse vibrations in strings.