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Fundamental systems and solutions of nonhomogeneous equations for a pair of mixed linear ordinary differential equations

Part of: General theory in ordinary differential equations

Published online by Cambridge University Press:  09 April 2009

M. Venkatesulu  and
T. Gnana Bhaskar
M. Venkatesulu
Affiliation:
Sri Sathya Sai Institute of Higher LearningPrasanthinilayam-515 134, A.P., India
T. Gnana Bhaskar
Affiliation:
Sri Sathya Sai Institute of Higher LearningPrasanthinilayam-515 134, A.P., India
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Abstract

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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 nonhomogeneous 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 systematic study of these new classes of problems is being developed. In the present paper, we construct the fundamental systems and exhibit the forms of solutions of nonhomogeneous problems associated with the pair (L1, L2).

MSC classification

Secondary: 34A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 1 , August 1990 , pp. 161 - 173
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Boyles, C. Allan, Acoustic waveguides, applications to oceanic sciences, (Wiley, New York, 1984).Google Scholar
[2]Coddington, E. A. and Levinson, N., Theory of ordinary differential equations (McGraw-Hill, New York, 1955).Google Scholar
[3]Ghosh, P. K., The mathematics of waves and vibrations, (Macmillan India, Delhi, 1975).Google Scholar
[4]Noda, K., ‘Optical fiber transmission’, Studies in telecommunication, vol. 6, edited by Noda, K., (North Holland, Amsterdam, 1986).Google Scholar
[5]Stakgold, I., Green's functions and boundary value problems, (Wiley-Interscience, New York, 1979).Google Scholar
[6]Venkatesulu, M. and Bhaskar, T. Gnana, ‘Solutions of initial value problems associated with a pair of mixed linear ordinary differential equations, in J. Math. Anal. Appl. (to appear).Google Scholar
[7]Venkatesulu, M. and Bhaskar, T. Gnana, ‘Selfadjoint boundary value problems associated with a pair of mixed linear ordinary differential equations’, J. Math. Anal. Appl. (to appear).Google Scholar