J Austral Math Soc Ser A 49 pp161--173, 1990.

Fundamental Systems and Solutions of Nonhomogenous Equations for a Pair of Mixed Linear Ordinary Differential Equations

M. Venkatesulu and T. Gnana Bhaskar

Abstract

Two different ordinary differential operators L₁ and L₂ (not of the same order) defined on two adjacent intervals I₁ and I₂, respectively, with certain mixed conditions at the interface are considered. These problems are encountered in the study of 'acoustic waveguides in ocean', 'transverse vibrations in nonhomogenous strings', etc. A complete set of physical conditions on the system give rise to three types of (selfadjoint) boundary value problems associated with the pair (L₁, L₂). In a series of papers, a symmetric study of these new classes of problems is being developed. In the present paper, we construct the fundamental systems nd exhibit the forms of solutions of nonhomogenous problems associated with the pair (L₁, L₂).

1980 AMS Subject Classification (1985 Revision): 34A99

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Authors

M. Venkatesulu

T. Gnana Bhaskar

Sri Sathya Sai Institute if Higher Learning, Prasanthinilayam-515 134, A.P., India.