Abstract
In this chapter we use the dynamic programming techniques as applied to the various problems and arrive at the structure of the solutions of the second order equations without solving them. The variation diminishing properties of the Green’s functin, the unimodal nature of the solutions of the Sturm- Liouville equations are derived in Sections 1 and 2. In Section 3, variational equations for the characteristic functions and characteristic values are obtained, treating one of the limits of the interval of integration as the imbedding parameter.
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References
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© 1986 D. Reidel Publishing Company
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Bellman, R., Vasudevan, R. (1986). Dynamic Programming and Solution of Wave Equations. In: Wave Propagation. Mathematics and Its Applications, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5227-0_11
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DOI: https://doi.org/10.1007/978-94-009-5227-0_11
Publisher Name: Springer, Dordrecht
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