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 defined on an interval [d1, d2] and 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.
Highlights
A CLASSICAL APPROACH TO EIGENVALUE PROBLEMS ASSOCIATED WITH A PAIR OF MIXEDSri Sathya Coal Institute of Higher Learning Department of Mathematics and Computer Science
In studies of acoustic waveguides in ocean [1], buckling of columns with variable cross sections in applied elasticity [9], transverse vibrations in nonhomogeneous strings [2], etc., we encounter a new class of problems of the type d2yl dx2 ql(x)Yl "Yl defined on an interval [dl, d2] and L2y2 d2y2 dx 2 + q2(x)Y2)Y2, Printed in the U.S.A. (C)2000 by North Atlantic Science Publishing CompanyM
In most of the cases, the complete set of physical conditions give rise to eigenvalue problems associated with the pair (L1,L2)
Summary
Sri Sathya Coal Institute of Higher Learning Department of Mathematics and Computer Science. 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 Llyldy -d-2-y2l-rUl(X)Yl- "Yl defined on an interval [dl,d2] and. + q2(x)y2 .y2 on the adjacent interval [d2, d3] satisfying certain matching conditions at the interface point x- d2. In Part I, we constructed a fundamental system for (L1,L2) and derive certain estimates for the same. In Part II, we shall consider four types of boundary value problems associated with (L1,L2) and study the corresponding spectra
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