Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 2, Pages 205-214
doi:10.1155/S1048953301000168
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 515134, Andhra Pradesh, India
Received 1 February 1995; Revised 1 December 1999
Copyright © 2001 M. Venkatesulu 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
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.