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Journal of Applied Mathematics and Stochastic Analysis
Volume 15 (2002), Issue 2, Pages 181-187
http://dx.doi.org/10.1155/S1048953302000163

A classical approach to eigenvalue problems associated with a pair of mixed regular Sturm-Liouville equations II

Sri Sathya Sai Institute of Higher Learning, Department of Mathematics and Computer Science, Prasanthinilayam , Andhra Pradesh 515134, India

Received 1 February 1995; Revised 1 February 2000

Copyright © 2002 Hindawi Publishing Corporation. 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

In the studies of acoustic waveguides in ocean, buckling of columns with variable cross sections in applied elasticity, transverse vibrations in nonhomogeneous strings, etc., we encounter a new class of problems of the type L1y1y1+q1(x)y1=λy1 defined on an interval [d1,d2] and L2y2y2+q2(x)y2=λy2 defined on the interval [d2,d3] satisfying certain matching conditions at the interface point x=d2.

Earlier, in Part I, we constructed a fundamental system for (L1,L2) and derived certain estimates for the same.

Here, in Part II, we consider four types of boundary value problems associated with (L1,L2) and study the corresponding spectra.