A classical approach to eigenvalue problems associated with a pair of mixed regular Sturm-Liouville equations I. (2001) - Venkatesulu, M.; Baruah, Pallav Kumar
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.