A classical approach to eigenvalue problems associated with a pair of mixed regular Sturm-Liouville equations I. (2000)

• Record Type: Journal Article
• Authors: Venkatesulu, M.; Baruah, Pallav Kumar
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 13:Number 3(2000)
• Page Start: 303
• Page End: 312
• Publication Date: 2000
• Subjects: Sturm-Liouville equations -- interface boundary conditions -- initial value problems -- matching conditions -- fundamental system -- eigenvalue problems -- estimates -- inequalities; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953300000277
• Languages: English
• ISSNs: 1048-9533

Abstract

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.