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

M. Venkatesulu and Pallav Kumar Baruah

International Journal of Stochastic Analysis, 2000, vol. 13, 1-10

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 L 1 y 1 = − d 2 y 1 d x 2 + q 1 ( x ) y 1 = λ y 1 defined on an interval [ d 1 , d 2 ] and L 2 y 2 = − d 2 y 2 d x 2 + q 2 ( x ) y 2 = λ y 2 on the adjacent interval [ d 2 , d 3 ] satisfying certain matching conditions at the interface point x = d 2 .

Here in Part I, we constructed a fundamental system for ( L 1 , L 2 ) and derive certain estimates for the same. Later, in Part II, we shall consider four types of boundary value problems associated with ( L 1 , L 2 ) and study the corresponding spectra.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:565868

DOI: 10.1155/S1048953300000277

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