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Journal of Applied Mathematics and Stochastic Analysis
Volume 13, Issue 3, Pages 303-312
http://dx.doi.org/10.1155/S1048953300000277

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

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

Received 1 February 1995; Revised 1 December 1999

Copyright © 2000 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 non-homogeneous strings, etc., we encounter a new class of problems of the type L1y1=d2y1dx2+q1(x)y1=λy1 defined on an interval [d1,d2] and L2y2=d2y2dx2+q2(x)y2=λy2 on the adjacent interval [d2,d3] satisfying certain matching conditions at the interface point x=d2.

Here in Part I, we constructed a fundamental system for (L1,L2) and derive certain estimates for the same. Later, in Part II, we shall consider four types of boundary value problems associated with (L1,L2) and study the corresponding spectra.